Both of these words are prepositions. However, “after” is often used incorrectly.
For example, this is incorrect: “I will see you after”. After what?
“After” requires an object, as in this example: “I will see you after the opera”.
“Afterwards”, on the other hand (por otro lado) does not need an object. “Afterwards” refers to something that you have already communicated:
“I am going to the opera house in Santa Cruz and I will see you afterwards”.