Changing virtual desktops works for me, no patches needed. I have to use it often because of how many games don’t understand multiple monitors.

Technically they have some differences, but the biggest from a user’s perspective is how they are delivered and by whom. Wine is manually installed by you from your distro’s package repo. Proton is provided by steam when you install a windows game on a Linux steam instance. If one breaks then you complain to the relevant party.