What is the difference between an hour angle and an azimuth angle? When I see illustrations of the two, the angles look very similar.
Hour angle is measured along the celestial equator: 0h is the local meridian, 6h is in the western sky, etc. Lines of equal hour angle converge at the celestial poles.
In other words, the two angles are measured around different axes. The angle between those axes is the complement of the observer's latitude.