Hope this helps to explain.
All azaleas are rhododendrons but not all rhododendrons are azaleas. Azaleas have been reclassified and are now in the genus Rhododendron. There are no clear cut lines for distinguishing all azaleas from all rhododendrons but here are a few characteristics to look for.
True rhododendrons have 10 or more stamens which is 2 per lobe. Azaleas usually have 5 stamens or 1 per lobe. Azaleas have 5 lobes in a flower.
Azaleas tend to have appressed hairs which is hair parallel to the surface of the leaf. This is particularly true along the midrib on the underside of the leaf. It is easily seen in "evergreen" azaleas. True rhododendrons instead of hair are often scaly or have small dots on the under side of the leaf. Azalea leaves are never dotted with scales and are frequently pubescent.
Many azaleas are deciduous. True rhodi's are usually evergreen with the exceptions of R. mucronulatum and R. dauricum.
Azaleas have tubular funnel or funnel shaped flowers. Rhodi flowers tend to be bell-shaped.
Note: This information was obtained from:
Dirr, Michael A. 1998. Manual of Woody Landscape Plants. 5th edition. Champaigh, Ilinois: Stipes Publishing.
Greer, Harold. 1996. Greer's Guidebook To Available Rhododendrons. 3rd. edition. Eugene, Oregon: Offshoot Publications.