Different resolution when connecting to Mac remotely
There's a subtle difference in the 2 technologies-- and kind of a misnomer.

Apple's remote screen sharing technology is based on VNC -- Virtual Network Computing. You'd think this would be a virtualized technology that would provide you with whatever screen resolution you wanted, right?

And Windows RDP -- Remote Desktop Protocol -- it would only give you what appeared on a remote desktop, right?

Wrong and wrong.

Apple's VNC-based Screen Sharing will show you what the user's preferences are set to. This is great for supporting a remote user -- you see exactly what they see, even if they have multiple monitors, you can pick and choose which one (or both) that you want to see.

And if there's someone already logged on to the system and you're connecting from another Mac? You're given the choice of whether you want to connect to their account's display, or use your own account's preferences. Multiple users simultaneously on one Mac, even with different screen resolutions.

So the trick is, set your account's preferences to what you want to see remotely; by default, that's going to be the native screen resolution your MacBook Pro supports. I think that once you've set those on your desktop, you're only given the option of scaling it on the Screen Sharing session if you're logged in with a user account not associated with a physical display (the Display preferences shows your remote session as an Unknown Display.) 

But changing the resolution to something that's not reflected on the remote display? That's virtualized technology only supported by Remote Desktop.

Yes, confusion, caused by poor choices in names. Apple's use of Screen Sharing is probably the most appropriate name of them all.