These two nouns are basically synonyms. Personally, I've seen both being used to refer to a small part of a longer text. I'd say 'excerpt' sounds more specific, since the verb 'to extract' can be used in multiple contexts. I hope it helps!

Extract is to pull something out. Excerpt is a group of words that are part of a larger written document. Examples; My dentist will extract my tooth tomorrow. The seeds are extracted from the fruit before feeding the fruit to a baby. This poem is an excerpt from a book. I will show my sick friend an excerpt from a medical book pertaining to their illness.