Rising and Setting of stars
Let us first ask the question: “how high in the sky do we see the Celestial Pole”? Well that depends on where you are on Earth, more specifically on your latitude or angular distance from the equator.
At high latitudes (e.g. northern Europe, northern America’s, or South Africa, Australia) you will see the celestial pole quite high in the sky. It will be extreme when you are precisely on the north or south pole, when you will see the celestial pole straight above you in the zenith.
Precisely at the equator you will theoretically see both poles at the horizon, but practically you won’t see either of them.
The angle (altitude) you see the Celestial Pole above the horizon
is equal to the latitude of your position (see diagram).
Depending on where you are on Earth, you could see some stars never rise or set, but always above the horizon. These stars are called circumpolar stars. Time exposure photos can give spectacular results, showing the position of the Celestial Pole.
Stars that are further away from the Celestial Pole will rise and set. We don't have a special name for those, but you could call them rising-and-setting stars.