Altitude is height above the horizon
Altitude measures angular distance above or below the observer’s horizon. An object on the horizon is near 0°; the zenith is +90°.
Sources: U.S. Naval Observatory — Computing Altitude and Azimuth
Azimuth is direction around the horizon
Azimuth measures direction along the horizon, usually clockwise from true north. Together, altitude and azimuth give an intuitive local position for a celestial object.
Sources: U.S. Naval Observatory — Computing Altitude and Azimuth
They change with observer and time
To convert from equatorial coordinates to local horizon coordinates, you need sidereal time plus the observer’s latitude and longitude. That is why a personal sky chart is genuinely geospatial.
Sources: U.S. Naval Observatory — Computing Altitude and Azimuth