All perfect praise be to Allah
Basically, shahadah is a way to get a person's consent on whether or not he believes in these 2 things.
Both of these kalamas can be found in books of ahadees as complete one sentence quoted. For reference, people usually call لا إله إلا الله محمد رسول الله first kalma and أَشْهَدُ أَنْ لاَ إِلَهَ إِلاَّ اللَّهُ وَأَشْهَدُ أَنَّ مُحَمَّدًا عَبْدُهُ وَرَسُولُهُ second kalma(at-least in our region).
Let me first quote the references for their presence as a whole in ahadees:
For first kalma:
عَنِ النَّبِيِّ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ قَالَ : أَنْزَلَ اللَّهُ تَعَالَى فِي كِتَابِهِ ، فَذَكَرَ قَوْمًا اسْتَكْبَرُوا فَقَالَ : إِنَّهُمْ كَانُوا إِذَا قِيلَ لَهُمْ لا إِلَهَ إِلاَّ اللَّهُ يَسْتَكْبِرُونَ ، وَقَالَ تَعَالَى : إِذْ جَعَلَ الَّذِينَ كَفَرُوا فِي قُلُوبِهِمُ الْحَمِيَّةَ حَمِيَّةَ الْجَاهِلِيَّةِ فَأَنْزَلَ اللَّهُ سَكِينَتَهُ عَلَى رَسُولِهِ وَعَلَى الْمُؤْمِنِينَ وَأَلْزَمَهُمْ كَلِمَةَ التَّقْوَى وَكَانُوا أَحَقَّ بِهَا وَأَهْلَهَا ، وَهِيَ لا إِلَهَ إِلاَّ اللَّهُ مُحَمَّدٌ رَسُولُ اللهِ اسْتَكْبَرَ عَنْهَا الْمُشْرِكُونَ يَوْمَ الْحُدَيْبِيَةِ يَوْمَ كَاتَبَهُمْ رَسُولُ اللهِ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ فِي قَضِيَّةِ الْمُدَّةِ
کتاب الاسماء والصفات للبیہقی:ـجلدنمبر 1صفحہ نمبر263حدیث نمبر195۔ ناشر:مکتبة السوادی، جدة ،الطبعة الأولی -- درجہ: صحیح ۔
This is along hadees and purpose of quoting full text is just to make it easy if anyone want to search more about it. You can read whole complete first kalma in it(in bold).
Now, coming to second kalma, this is the kalma, about which prophet ﷺ specifically said, if one believes in this and dies, that person will go to jannah:
من مات و ھو یشھد ان لا الہ الا اللہ و ان محمد رسول اللہ صادقا من قلبہ دخل الجنۃ ۔
صحیح ابن حبان :ص:366 ج : 1
Explanation of hadees: This does not mean that everyone who believes in this kalma will go straight to jannah (except whoever allahAllah will to send), this means that every believer will end up in jannah after completing his/her punishment, this is proved form other sources(ahadees etc) but discussion about it is out of the scope of the question.
The requirement for becoming muslim is giving consent and believing in what these two kalmas means. Basic meaning is same in both of these kalmas, only difference is that in the second one, there is a stated consent that i believe in this. And this same kalma was used by the prophet ﷺ and all his companions(and all muslimsMuslims after them) to get consent from a new muslimMuslim. So, it should be used for this purpose, preferring over any other kalma. Although, most scholars agree that first kalma is also sufficient for the consent. (As stated in hadees in which Hazrat Huzaifa killed a person in war who said la ilaha il-Allah just before he was killed, and prophet became very angry on him that he killed a believer. ref)
Lastly, about the last part of your question concerning about the shahadah/kalma of shia, i am no one to speak on their behalf, they should explain it themselves. I can just say that the above 2 kamlas(1st and 2nd kalma) are proved from ahadees as is. ANdAnd was used at the time of prophet too, the part shia append in the end of kalma is surely appended by them after his(Ali R.A) death.
