Disclaimer: I'm a Korean-American heritage speaker (not formally trained as a Korean linguist or teacher). But these are the differences as far as I understand them. 기억 comes from the verb "기억하다". Basically, it's used to refer to remembering something. It's a word you will likely encounter more when speaking. Like when you say "I remember that." "응, 기억해" I'm not an expert, but I believe it's generally used as a verb. ex) "그 사람 만난것 기억해." "I remember meeting that person." 추억 means "memory" or "memories." Or in another more literary sense, "recollections." ex) "공원을 보니 어린 시절의 추억이 떠오른다." "Seeing the park reminded of the times (recollection, memories) of my childhood."

I think of it this way. - 기억 = memory or recollection of any kind. It is widely applicable but most often used for factual memory. - 추억 = fond memory. It implies emotional, nostalgic memory. So 기억 has a factual and dry connotation of being able to recall. 추억 on the other hand is about something one remembers fondly as if wanting to go back to the time, not the ability or fact. Thus we say 기억력, memory(as an ability), but 추억력 doesn't exist. If it's used about something unpleasant (as in 살인의 추억), it is usually an ironic expression.

memory: the faculty by which the mind stores and remembers information. like how was your childhood, or something funny that happened to you. Recollection is either the process of remembering something or a specific memory. the action or faculty of remembering or recollecting something. "to the best of my recollection no one ever had a bad word to say about him"