Image and Likeness of God
The Image of God and the Likeness of God refer to similar, but distinct aspects to how God made human beings. These days, the former is almost always conflated with the latter and is used to refer to what is actually God's Likeness, rather than God's Image.
Image of God
The Image of God refers to human form (the human body itself) being made to look like God. Or it refers to Jesus looking like God in the most literal sense possible [John 14:9]. The words for "image" in the Bible are "selem" in Hebrew and "eikon" in Greek. Both always refer to a visual representation. There is no biblical evidence to support any claims that the words for "image" ever refer to anything other than a visual representation when it comes to man being made in God's Image.
It is first mentioned that God created man in his image in Genesis 1:26-27, where Torah gives an overview of each of the seven days of the creation week. This image is called "very good" in Genesis 1:31 when God calls everything that he created (including the image of himself that he created) "very good". Mankind being made in God's Image is the reason that God institutes the death penalty for murder in Genesis 9:6, and is also the reason given for several other things throughout Scripture. God's Image is also emphasized in the Bible more than God's Likeness.
Genesis 5:3 is often used as a proof-text for the heresy that the image of God was somehow lost or marred by The Fall, but regained through faith in Jesus. But there is no indication anywhere in Scripture that this is indeed the case. At most, it proves that Adam was reproducing after his kind, just like how all of the plants and animals reproduce after their kinds.
Likeness of God
The Likeness of God refers to the fact that human beings were made to share similarities with God that do not have anything to do with what mankind was made to look like. The words translated as "likeness" in the Bible are "demuth" in Hebrew and "homoiosis" in Greek. It is stated in Genesis 1:26 and Genesis 5:3 that man was made after God's Likeness (those verses also mention God's Image). Mankind was made to have some of God's attributes, such as emotion, reason, and creativity. Mankind did not lose God's Likeness during The Fall, but it was corrupted in such a way that mankind prefers doing evil rather than good. It is for this reason that children need to be taught to do good from a young age. Man being created in the likeness of God is the reason James gives in James 3:9 to not curse our fellow man.