The Ten Commandments in both places (Exodus 20:1-14, Deuteronomy 5:6-18) have two sets of Teamim known as Taam Haeliyon (the upper Taam), and Taam Hatachton (the lower Taam).
The Taam Eliyon consists mainly of the signs that come on top of the words and the Taam Tachton uses generally the signs that come underneath the text. Hence their names. Also, in the Eliyon the Teamim are generally of a higher pitch level than the Tachton. The difference between the tune not only affects the cantillation, but it makes a difference in the syntax. Whereas the Tachton, that originates in Eretz Israel, divides the text into verses, the Eliyon, that follows the Babylonian tradition, divides the text into commandments.
The widespread custom nowadays is that when reading privately to oneself (Shnaim Mikra Ve’Echad Targum) the Taam Tachton is used, and the Taam Eliyon is reserved only for the public reading in the synagogue.