My cassette model name doesn't seem to fit the actual cassette description.. (CS-HG50-9 and CS-HG500-10) I have a Ridley Fenix classic bicycle that I bought second hand online.
(all components are Shimano Tiagra) 

A year has passed and I figured I should really change the chain and cassette altogether. I didn't want to buy all the parts from the LBS since they're really overpriced so I decided to check the model name and just buy it online.

The first really weird thing I noticed was that the model name was CS-HG-9 but I had ten gears on the cassette.

Here's a photo: 

I thought this didn't really matter if I just bought a 9 speed cassette instead but then I saw that it's not recommended to put a 9 speed cassette if I have a 10 speed shifter.

The current cassette (which works well for me) is 12-28T and I found a CS-HG500-10 cassette online which is 10 speed 12-28T cassette (seems perfect for me).

My questions:


Will the CS-HG500-10 fit without any issues (with an HG 10 speed chain)?
I wasted time and money because of the incorrect model name, is it really incorrect or am I just confused?
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.