While shirk is associating anyone other than Allah, and Kufr is denying or concealing the articles of Imaan. So does it mean that denying tawheed, is tantamount to kufr. But kufr may not be shirk, e.g. denying Resurrection, can be Kufr but not shirk.
Kufr is the denial and concealment of the Truth such as those who deny the obligation of Salah, Zakah, Sawm, Hajj in case of being financially and physically able, and dutifulness to one's parents, and so on.
It is also like those who deny the prohibition of Zina (premarital sexual intercourse and/or adultery), consuming Khamr (intoxicants), and disobeying one‘s parents.
ALLAH (Glorified and Exalted be He) says
Here, ALLAH (Exalted be He) names their call upon things other than Him as Shirk and in Surah Al-Mu'minun, Allah (Exalted be He) names it Kufr.In Surah Al-Tawbah, ALLAH (Glorified be He) says,
Here, Allah (Exalted be He) calls the disbelievers as Kuffar and Mushriks. This indicates that a Kafir may be called a Mushrik and vice versa. There are many Ayahs and Hadith that stress the same meaning.
The Prophet (peace be upon him) said,
"Verily, between a man and Shirk and Kufr is the negligence of prayer." (Related by Muslim in his Sahih (authentic) book of Hadith on the authority of Jabir Ibn `Abdullah, may Allah be pleased with them).
He (peace be upon him) also said, "The covenant that distinguishes between us and them (the hypocrites) is Salah. Anyone who abandons it is a Kafir."
(Related by Imam Ahmad, Abu Dawud, Al-Tirmidhy, Al-Nasa'y, and Ibn Majah with a Sahih chain of transmission on the authority of Buraydah ibn Al-Hasib, may Allah be pleased with him).
Here is a good link regarding disscussion "What is the difference between mushrikeen and kuffaar? Are the Jews and Christians mushrikeen or kuffaar?."