My cassette model name doesn't seem to fit the actual cassette description.. (CS-HG50-9 and CS-HG500-10)
There are usually little compatibility problems for nine or ten speed cassettes. You may choose from a large set of cassettes that work for you.

Shimano, SRAM, and Sunrace use the same standards. (The exception are Campagnolo. If there is a a cassette with a 10 teeth cog it would require a specific free hub body.)

The length of your rear derailleur's arm limits your choice of largest cog. You may check the capacity of your derailleur online. Or count the teeth on your present largest cog. Use that count as upper bound.

The lock ring of all these cassettes is interchangeable. We may never found out why yours has a different designation as the cassette. It might be as trivial a reason as a spare for a fumbled original part. Simple consequence: don't rely on it without checking.