Trying to determine what type of pool I have

Hi pool experts,
I have recently purchased a house with a pool (first time owning a pool). It appears to me to be a concrete pool (or something similar). It is not vinyl, pvc, fibreglass etc.
The original owner told me that he used to paint the pool once a year, but then had the pool rebuilt in natural stone, so it now no longer needs painting.
That makes sense, however I'm trying to confirm whether the pool is actually built from natural stone.
I am not talking about the decking, or any features, or anything like that - just the actual pool itself (the walls and floor).
If it were natural stone, what would it look like??
I figured it would look tiled (ie. with natural stone tiles) - but it does not look tiled.
Is it possible that it was tiled with natural stone and then covered/sealed with something that looks like concrete, or shotcrete, or something?? But that doesn't make sense.
Currently the surface looks to me like a type of plaster. It is comfortable to swim in, but if you spend an hour or two in the pool jumping around a lot your feet tend to get a bit sore - with little abrasions from the slightly rough surface.
I am asking all this as I was thinking about painting the pool - to give it a more appealing look, as its a bit drab and dirty - but was told by the original owner NOT to paint the pool.
Unfortunately I am no longer touch with the original owner - otherwise I could ask him.
Many thanks for any advice you could share.
Best
Tady