Right Ascension and Declination are celestial coordinates based on the assumption that the sky is a virtual sphere with the pole star (Polaris) at the top center of the sphere. So RA and Decl. are related to the sky and the time.
Azimuth and Altitude are spherical coordinated derived from a specific point on the ground. A point in the sky is at some altitude above the horizon and some azimuth angle relative to a chosen reference line (typically north-south).
Any given object or point in the sky exists at some coordinates in both systems at once, but the relationship between the two is a complex problem in spherical geometry.
They are measurements from two different systems of coordinates.
Right ascension and declination tell of a celestial object’s position on the celestial sphere, in relation to other ‘fixed’ stars. Unless the object moves in relation to fixed stars (for example a planet moves over the year, when compared to fixed stars), the right ascension and the declination of a star does not change a lot over long periods.
Azimuth and altitude are very local things. They are measurements on the observer’s local celestial sphere. The main point is the zenith, and the (theoretical) horizon is located at 90° from the zenith.
altitude is the local apparent angle that an object has above the horizon.
The azimuth is the direction you face when looking at the object.
Because of Earth’s rotation, the whole celestial sphere appears to turn westward (roughly 15° per hour). Therefore, even it the observer is looking at a ‘fixed’ star (right ascension and declination don’t change), his local measurements of altitude and azimuth will constantly change.