The etymology of English "cassette" appears to come from the French word for "little box", which makes sense for tape cassettes but not for bicycle gearing. Considering that bicycle cassettes were invented in the 70s whereas tape cassettes are from the 60s, I'd be curious to know the reason for the name.
Little box to hold a removable piece or mechanism, so seems a bit of a stretch unless cassette gears pop out for replacement? There were far earlier uses. The box that held the glass plates in early plate cameras was called a cassette.
https://www.etymonline.com/word/cassette