Eureka! One is a transitive adverb, and can be used with or without a subject, and afterwards is an intransitive adverb and cannot be used with a subject of adverb. "He read a book afterward", where "a book" is a subject" but "they lived afterwards", without a subject. The first is a transitive, and the second is an intransitive adverb.

They do have the same meaning. 'Afterward' is more unusual than 'afterwards', although ( like 'toward') you might come across it in some North American contexts. It is rarely used outside N.America.

Afterward - and afterwards are different parts of speech. For example: he read the book afterward BUT they lived happily afterwards. They are two different types of adverbs, that's what I am trying to say, but I cannot put my finger on it. AND "afterwards" is more poetic/archaic.

after