After is a preposition that will be followed by a noun or pronoun. We're going for ice cream after school. "School" is the noun here. I'm going to the gym after work. "Work" is the noun here. Afterwards is an adverb. It will not be followed by a noun or pronoun. It's usually used when there is prior context. My family is seeing a play tonight. We're going to meet at the diner afterwards. There was a big game at the arena last night. All my friends went to the diner afterwards. After that is really just "after" with the demonstrative pronoun "that." Just substitute whatever "that" refers to. We're going dinner tonight, and then we're going to the movies after that. (That = dinner) I hope this helps.