Plumbing code (at least the ones I look at - your local may or may not be the same) expects a 2" minimum drain for a shower that's not in a tub. That's why all shower drains you can find are 2" connections.
A tub drain can be 1.5" - and depending how your local code and local inspectors line up, you might find you can only have a shower that's in a tub, unless you rent a jackhammer and replace the pipe.
Better to find that before you have a non-compliant shower actually installed.
If the previous fixture here was a shower and if your project can be viewed as "replace with same" rather than "remodel" you MIGHT be able to get it "grandfathered" to pass. Looks to me from the pictures like "remodel and meet current codes as a result", but I'm not your Local Authority Having Jurisdiction's inspector. They are the folks that have to be happy, and if they are not happy they can tell you to rip it out.
You could rent a drain camera and get an idea of how far it goes before connecting to a larger drain pipe. Normally not that far in a bathroom group, so the amount of jackhammering may be quite manageable once you accept that it's possible and may be required.
Having clarified that the LAHJ has allowed it as a grandfathered use
You pretty much have to go with any of several possible adapters (or combinations of adapters) from 1.5" copper sweat to whatever your 2" drain expects. A "Fernco" (rubber coupling, Fernco is a brand often used as shorthand for the class of product) will do it on one piece. I'm a bit squirrely about putting those where they are hard to get to unless they are buried in the ground. A 1.5" pipe thread to copper sweat and a 2"-1.5" pipe thread reducer will do it. If wanting PVC or ABS, PVC/ABS glued socket to pipe thread reducing fittings exist.
Make sure you have good cleanout access to the point where the reducer will live - there's a reason that reducing drain line sizes is normally forbidden, and the reason is that they are a source of clogs due to the restriction in the pipe. Right under the shower drain grate is a far better place for it than on the far side of a trap.