In TOS, there are numerous references to "tapes" as a recording medium:

I hope that the phrase is actually just out-of-date terminology that got stuck (like how we refer to motion pictures as "films" even though they're probably not shot or transmitted on actual film any more), and not actual magnetic ribbons used for data storage.

We really do need some more up-to-date Klingon terminology for modern day technologies. Does anyone even talk about "cassettes" any more?
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