MC for Windows and MC for Mac are licensed
separately (each has its own fee). To use the same license on both Windows and OSX, you need to have purchased a
Master License. If you didn't, and only bought one or the other, it won't work, though you can upgrade to the Master License for a modest cost (much less than buying the two licenses separately).
Assuming you already had the Master License, then make sure you are running the latest version of MC on both machines. This may not be the one you already have, as they release new ones all the time. That will fix the MC21 versus MC20 thing. They've just updated the internal licensing model, and will eventually release the first betas of MC21. The licenses they're now selling aren't compatible with older versions of MC20, but are compatible with the latest-and-greatest versions.
That should be, as of today:
* MC for Mac 20.0.124, available here:
http://yabb.jriver.com/interact/index.php?topic=98430.0* MC for Windows 20.0.123, available here:
http://yabb.jriver.com/interact/index.php?topic=98427.0Don't worry about using up the restores. They can be reset later if you ever run out for legitimate reasons (like this). That limit is to keep people from sharing licenses with friends and whatnot.