I changed the wheels on my bike and while doing so put a new 10 speed cassette on the new wheel.
This would mean I would have shiny new wheels on my bike and the old wheel with the old cassette to use on the turbo (I really hate changing my tyres over all the time!!)

However, now my gears are not shifting correctly with the new wheel / cassette.

The old cassette was a shimano 10 speed 12-25 and the new one is a SRAM 1070 10 speed 12-27.

I stupidly thought I would be able to swap between the two with no issue.

When I change the gears with the new wheel they are pretty rough sounding. It shifts up to the 27 cog but will not shift all the way to the 12 - it will not go onto the two smallest cogs.

I wonder if the problem is with the hub itself, I know it can be adjusted so does it just need to be aligned to suit my bike?
I guess if I need to index / adjust the gears to match the new wheel then the old one won't work properly when I want to use the turbo?

Things are never straight forward!!

So you're running an old chain on a new cassette? That generally won't help matters, although your 'won't go into all the gears' issue sounds like indexing, so a quick tweak of the limit screw should sort it.

Doesnt the Sram have a different ratio on the shift lever to the Shimano?

SRAM and Shimano cassettes are interchangeable (shifters & deraileurs are not). The indexing always needs some tweaking when swapping over, especially if they are different size cassettes, but with such a big difference you might benefit from a spacer on the hub to get the chain line sorted.

The rest of the system is SRAM rival. Just the original cassette was shimano for some reason.

The wheel is 11 speed compatible so it has a spacer on it for the 10 speed cassette.

Will stick a new chain on it tomorrow and take it from there. Worst case I can drop it at the LBS.

If its just the cassette you have changed it will need indexing every change of wheel. And the cage hight adjusted.

I put it up on the stand this morning and was managing to get it in all the gears without changing anything but was sounding rough.
I then noticed it has a 9 speed chain fitted. Surprised my LBS put a nine speed with a ten speed cassette. Even more surprised that my last 10 speed cassette did not care!!
So new chain it is!