Kufr is not automatically shirk, but major shirk is automatically kufr. In addition, kufr is not restricted solely to rejecting Islam; rather, kufr comprises nullifying Islam, too, which can happen while still accepting or embracing the tenets of the Muslim faith.
Kufr may be used along with shirk to mean the same thing:
حَدَّثَنَا أَبُو غَسَّانَ الْمِسْمَعِيُّ، حَدَّثَنَا الضَّحَّاكُ بْنُ مَخْلَدٍ، عَنِ ابْنِ جُرَيْجٍ، قَالَ أَخْبَرَنِي أَبُو الزُّبَيْرِ، أَنَّهُ سَمِعَ جَابِرَ بْنَ عَبْدِ اللَّهِ، يَقُولُ سَمِعْتُ رَسُولَ اللَّهِ صلى الله عليه وسلم يَقُولُ: بَيْنَ الرَّجُلِ وَبَيْنَ الشِّرْكِ وَالْكُفْرِ تَرْكُ الصَّلاَةِ
— NOTE: My own translation, so treat with care:
Narrated on the authority of Abu Al-Zubair through Jabir ibn 'Abdullah saying through the Prophet (ﷺ): Between a man and shirk [polytheism] and kufr [lack of belief] is the abandonment of salat [prayers].
— Sahih Al-Bukhari 1/154
Al-Nawawi in Sharh Sahih Muslim (Arabic: شرح النووي على مسلم) said in his commentary about the hadith above:
ثم إن الشرك والكفر قد يطلقان بمعنى واحد وهو الكفر بالله تعالى ، وقد يفرق بينهما فيخص الشرك بعبدة الأوثان وغيرها من المخلوقات مع اعترافهم بالله تعالى ككفار قريش ، فيكون الكفر أعم من الشرك
— NOTE: My own translation, so treat with care:
Then shirk and kufr may be used as labels of the same meaning, and may be used to differentiate between polytheism idolatry from other creatures that recognizing Allah, as in the case of the disbelievers of Quraish. Therefore, Kufr is more general than shirk.
Ibn Hazm in his Al-Fasl fi Al-Milal wa Al-Ahawa' wa Al-Nihal (Arabic: الفصل في الملل والأهواء والنحل), Vol.3, pp. 119 said:
بل الجحد لشيء مما صح البرهان أنه لا إيمان إلا بتصديقه كفر والنطق بشيء من كل ما قام البرهان أن النطق به كفر كفر والعمل بشيء مما قام البرهان بأنه كفر كفر
— NOTE: My own translation, so treat with care:
Rather, rejecting what is proven to be an essential part of faith, without which there is no faith, is kufr; uttering anything that is proven to be kufr is considered kufr; and acting in a manner that is proven to be kufr is kufr.
All beliefs that you mentioned in your question constitute some form of shirk, but there there are other forms of kufr that are not necessarily based on shirk. For instance:
- Rejecting the truth
- Partial belief in the truth
- Nifaq (hypocrisy)
- Ridiculing aspects of the religion
Rejecting the truth
This is somewhat similar to not accepting the truth (from an Islamic perspective, as ascribed to be true by the sources accepted to Muslims, i.e., the Qur'an and the Sunnah), the whole truth, and nothing but the truth. That is, not believing in the truth; or believing in the truth, but hiding it or hiding the belief in it; or believing in the truth, without rejecting the untruth.
Not believing in the truth may arguably be considered a form of shirk, as one would typically introduce rivals or partners to Allah in the process. An example of this situation is when the disbelievers in Quraish, and in specific Abu Jahl, told the Prophet (ﷺ) that they did not consider him a liar, but they considered his message to be untrue (refer to Qur'an 6:33). I will let you be the judge of whether this is driven by shirk, or otherwise. Allah describes them as transgressors.
Rejecting the truth while knowing it to be the truth is kufr, but there is no clear form of shirk in this situation. In the Qur'an, Allah tells us about how Bani Isra'el rejected the truth (the Qur'an) that they were well informed about beforehand. He then calls them kafereen (disbelievers):
وَلَمَّا جَاءَهُمْ كِتَابٌ مِنْ عِنْدِ اللَّهِ مُصَدِّقٌ لِمَا مَعَهُمْ وَكَانُوا مِنْ قَبْلُ يَسْتَفْتِحُونَ عَلَى الَّذِينَ كَفَرُوا فَلَمَّا جَاءَهُمْ مَا عَرَفُوا كَفَرُوا بِهِ فَلَعْنَةُ اللَّهِ عَلَى الْكَافِرِينَ
And when there came to them a Book from Allah confirming that which was with them — although before they used to pray for victory against those who disbelieved — but [then] when there came to them that which they recognized, they disbelieved in it; so the curse of Allah will be upon the disbelievers.
— Qur'an 2:89
Not rejecting the untruth is also widely accepted through scholarly consensus as a form of kufr. For example, whoever does not regard kufr as kufr is himself a disbeliever.
Qadi Ayyad in his book (Arabic: الشفا بتعريف حقوق المصطفى), Vol. 2, P. 4, Ch. 3, pp. 603:
وقائل هذا كله كافر بالإجماع على كفر من لم يكفر أحدا من النصارى واليهود ، وكل من فارق دين المسلمين أو وقف في تكفيرهم أو شك .
قال القاضي أبو بكر : لأن التوقيف والإجماع على كفرهم ، فمن وقف في ذلك فقد كذب النص والتوقيف أو شك فيه . والتكذيب أو الشك فيه لا يقع إلا من كافر
— NOTE: My own translation, so treat with care.
There is scholarly consensus that one is a disbeliever if one does not regard any of the Jews or Christians as disbelievers, does not regard apostates as a disbeliever, does not take a stance on this issue, or is unsure about it. Denying or doubting this would not occur except from a disbeliever.
In this case, one may have the correct beliefs about the oneness of Allah, and may embrace the truth, the whole truth, but does not reject the untruth (either by accepting it, or being neutral to it), but one would still be considered to have committed kufr, with no acts of shirk being undoubtedly obvious (as it could be argued that the neutrality in this case stems from not fully accepting Allah's message; hence, associating partners to Allah who declare that accepting acts of kufr from others is not kufr).
Partial belief in the truth
In the Qur'an, Allah tells us about how Bani Isra'el rejected some of their prophets (based on arrogance, or disagreement). He then attributes kufr to them for doing so:
وَلَقَدْ آتَيْنَا مُوسَى الْكِتَابَ وَقَفَّيْنَا مِنْ بَعْدِهِ بِالرُّسُلِ وَآتَيْنَا عِيسَى ابْنَ مَرْيَمَ الْبَيِّنَاتِ وَأَيَّدْنَاهُ بِرُوحِ الْقُدُسِ أَفَكُلَّمَا جَاءَكُمْ رَسُولٌ بِمَا لَا تَهْوَى أَنْفُسُكُمُ اسْتَكْبَرْتُمْ فَفَرِيقًا كَذَّبْتُمْ وَفَرِيقًا تَقْتُلُونَ وَقَالُوا قُلُوبُنَا غُلْفٌ بَلْ لَعَنَهُمُ اللَّهُ بِكُفْرِهِمْ فَقَلِيلًا مَا يُؤْمِنُونَ
And We did certainly give Moses the Torah and followed up after him with messengers. And We gave Jesus, the son of Mary, clear proofs and supported him with the Pure Spirit. But is it [not] that every time a messenger came to you, [O Children of Israel], with what your souls did not desire, you were arrogant? And a party [of messengers] you denied and another party you killed. And they said, "Our hearts are wrapped." But, [in fact], Allah has cursed them for their disbelief, so little is it that they believe.
— Qur'an 2:87-88
There is no clear act of shirk in this case. The same applies to not believing in all scripture revealed by Allah, or believing in parts of the scripture and rejecting other parts (see Qur'an 2:85).
Allah narrates a story of two men from Bani Isra'el, where one owned two gardens of grapevines, palm trees, and other crops. In their discussion, the owner of the two gardens shows signs of doubt about Judgment Day, but then goes to strongly confirm that if there was such a thing as being brought back to life after death, he would without doubt be rewarded more in the afterlife:
وَدَخَلَ جَنَّتَهُ وَهُوَ ظَالِمٌ لِنَفْسِهِ قَالَ مَا أَظُنُّ أَنْ تَبِيدَ هَذِهِ أَبَدًا وَمَا أَظُنُّ السَّاعَةَ قَائِمَةً وَلَئِنْ رُدِدْتُ إِلَى رَبِّي لَأَجِدَنَّ خَيْرًا مِنْهَا مُنْقَلَبًا الَ لَهُ صَاحِبُهُ وَهُوَ يُحَاوِرُهُ أَكَفَرْتَ بِالَّذِي خَلَقَكَ مِنْ تُرَابٍ ثُمَّ مِنْ نُطْفَةٍ ثُمَّ سَوَّاكَ رَجُلًا
And he entered his garden while he was unjust to himself. He said, "I do not think that this will perish — ever. And I do not think the Hour will occur. And even if I should be brought back to my Lord, I will surely find better than this as a return. His companion said to him while he was conversing with him, "Have you disbelieved in He who created you from dust and then from a sperm-drop and then proportioned you [as] a man?
— Qur'an 18:35-37
The man who doubted a pillar of faith (Judgment Day) is considered to have committed an act of kufr, but no act of shirk is obvious.
Nifaq (hypocrisy)
The first five verses of Qur'an 2 describe the believers. Then Allah describes in the following verses what some of the munafiqeen (hypocrites) do, and labels them as those who do not believe:
إِنَّ الَّذِينَ كَفَرُوا سَوَاءٌ عَلَيْهِمْ أَأَنْذَرْتَهُمْ أَمْ لَمْ تُنْذِرْهُمْ لَا يُؤْمِنُونَ خَتَمَ اللَّهُ عَلَى قُلُوبِهِمْ وَعَلَى سَمْعِهِمْ وَعَلَى أَبْصَارِهِمْ غِشَاوَةٌ وَلَهُمْ عَذَابٌ عَظِيمٌ وَمِنَ النَّاسِ مَنْ يَقُولُ آمَنَّا بِاللَّهِ وَبِالْيَوْمِ الْآخِرِ وَمَا هُمْ بِمُؤْمِنِينَ يُخَادِعُونَ اللَّهَ وَالَّذِينَ آمَنُوا وَمَا يَخْدَعُونَ إِلَّا أَنْفُسَهُمْ وَمَا يَشْعُرُونَ
Indeed, those who disbelieve — it is all the same for them whether you warn them or do not warn them — they will not believe. Allah has set a seal upon their hearts and upon their hearing, and over their vision is a veil. And for them is a great punishment. And of the people are some who say, "We believe in Allah and the Last Day," but they are not believers. They [think to] deceive Allah and those who believe, but they deceive not except themselves and perceive [it] not.
— Qur'an 2:6-9
No clear act of shirk can be seen from those hypocrites.
Ridiculing aspects of the religion
A munafiq (hypocrite), during the time of the Prophet (ﷺ), said: "Why is it that our readers of the Qur'an are the hungriest among us, the biggest liars among us, and the most cowardly in the times of war?" When this reached the Prophet (ﷺ), this munafiq told the Prophet (ﷺ) that he was only conversing jokingly. Allah then revealed:
وَلَئِنْ سَأَلْتَهُمْ لَيَقُولُنَّ إِنَّمَا كُنَّا نَخُوضُ وَنَلْعَبُ قُلْ أَبِاللَّهِ وَآيَاتِهِ وَرَسُولِهِ كُنْتُمْ تَسْتَهْزِئُونَ. لَا تَعْتَذِرُوا قَدْ كَفَرْتُمْ بَعْدَ إِيمَانِكُمْ إِنْ نَعْفُ عَنْ طَائِفَةٍ مِنْكُمْ نُعَذِّبْ طَائِفَةً بِأَنَّهُمْ كَانُوا مُجْرِمِينَ
And if you ask them, they will surely say, "We were only conversing and playing." Say, "Is it Allah and His verses and His Messenger that you were mocking?" Make no excuse; you have disbelieved after your belief. If We pardon one faction of you - We will punish another faction because they were criminals.
— Qur'an 9:65-66
Allah in these verses calls those who ridicule or mock any aspect of the religion (Allah, his Messenger, or verses) as having committed kufr after being believers; any form of shirk is not readily obvious.
Al-Sa'di in his tafsir of the Qur'an that honoring Allah and His message is piety (see Qur'an 22:32); accordingly, mockery would be considered kufr. This is well demostrated in the verse below, where a clear form of shirk is not obvious:
وَقَدْ نَزَّلَ عَلَيْكُمْ فِي الْكِتَابِ أَنْ إِذَا سَمِعْتُمْ آيَاتِ اللَّهِ يُكْفَرُ بِهَا وَيُسْتَهْزَأُ بِهَا فَلَا تَقْعُدُوا مَعَهُمْ حَتَّى يَخُوضُوا فِي حَدِيثٍ غَيْرِهِ إِنَّكُمْ إِذًا مِثْلُهُمْ إِنَّ اللَّهَ جَامِعُ الْمُنَافِقِينَ وَالْكَافِرِينَ فِي جَهَنَّمَ جَمِيعًا
And it has already come down to you in the Book that when you hear the verses of Allah [recited], they are denied [by them] and ridiculed; so do not sit with them until they enter into another conversation. Indeed, you would then be like them. Indeed Allah will gather the hypocrites and disbelievers in Hell all together.
— Qur'an 4:140
