So, the term you are looking for is sidereal time. The sidereal day is 23 hours, 56 minutes and 4 seconds. Multiply the difference out and you see that the Earth's revolution is indeed responsible for adding an extra day to the apparent motion of the stars.
Also, the tilt of Earth's axis is why the sun's path moves up and down throughout the year, but has no impact on the stars: the north star, for example, is always in exactly the same place. The other stars just rotate around it.