I love how you conceptualise things based upon what seems to be your familiarity with DB cursors, stateful interfaces and other CS concepts. You're absolutely right, of course - it's just an interesting choice of conceptual frameworks to position your analogy within. I'm sure a non-programmer could also identify this property of cassettes as a medium, but they wouldn't be anywhere near as precise, nor use anything like that terminology...
I'm reminded of a character called Randy in a book called Cryptonomicon:
> To translate it into UNIX system administration terms (Randy's fundamental metaphor for just about everything)
I had a smile of recognition reading that, just like I had a smile of recognition reading yours. Stateful indeed. You might even term it a continuation.