During translating using tools, particularly Chinese to English, one often get twin translation results. For instance is your case. Let one worries down, when one encounters with such circumstances, then the first thing one has got to do is :
To break them words into pieces. This way, one will find the real differences between them two words. Making ones own interpretation is not always a bad idea because it always won't get too far as long as one is using the correct dictionary.
We know both words contain "enjoy"meaning, thus only pick that relates to "enjoy".
享受 = to enjoy. Or It means it relates to enjoying something.
享 = (v)to enjoy
受 = (v)to receive
欣赏 = to enjoy, but also to appreciate, and also to admire. Means that when you use 欣赏 in a sentence, then At the same time, the 欣赏 interpretation must match those three meanings.
欣 = (adj)gladly
赏 = (v)to view
So, do you see the difference now?