Botanically speaking there is no such species as an azalea, it is merely a term used by gardeners and nurserymen to refer to deciduous species and some evergreen species from Japan. Technically all azaleas are rhododendrons. However, we still call azaleas "azaleas"!
Azaleas can be deciduous (losing their leaves in winter) or evergreen and have one blossom per flower stem. Rhododendrons are all evergreen, grow larger than azaleas and have bigger, thicker, 'leathery' leaves. Rhododendron flowers are more bell shaped and each single flower stem has a cluster of these flowers.