A: 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.
Shirk is to devote the acts of worship to anything beside Allah (Exalted be He) such as those who seek the help of the dead, the absent, the Jinn, idols, the stars, and so on or those who offer sacrifices or make vows to them.
A Kafir (disbeliever) may be called a Mushrik (one who associates others with Allah in His Divinity or worship) and vice versa.
Allah (Glorified and Exalted be He) says,
And whoever invokes (or worships), besides All�h, any other il�h (god), of whom he has no proof; then his reckoning is only with his Lord. Surely! Al-K�fir�n (the disbelievers in All�h and in the Oneness of All�h, polytheists, pagans, idolaters) will not be successful.
Allah (may He be Praised) also says, Verily, whosoever sets up partners (in worship) with All�h, then All�h has forbidden Paradise to him, and the Fire will be his abode.
In Surah Fatir, Allah (Glorified and Exalted be He) says,
Such is All�h, your Lord; His is the kingdom. And those, whom you invoke or call upon instead of Him, own not even a Qitm�r (the thin membrane over the date-stone).
If you invoke (or call upon) them, they hear not your call; and if (in case) they were to hear, they could not grant it (your request) to you. And on the Day of Resurrection, they will disown your worshipping them. And none can inform you (O Muhammad صلى الله عليه وسلم) like Him Who is the All-Knower (of everything).
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,
They (the disbelievers, the Jews and the Christians) want to extinguish All�h‘s Light (with which Muhammad صلى الله عليه وسلم has been sent - Isl�mic Monotheism) with their mouths, but All�h will not allow except that His Light should be perfected even though the K�fir�n (disbelievers) hate (it).
It is He Who has sent His Messenger (Muhammad صلى الله عليه وسلم) with guidance and the religion of truth (Isl�m), to make it superior over all religions even though the Mushrik�n (polytheists, pagans, idolaters, disbelievers in the Oneness of All�h) hate (it).
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). May Allah grant us success!