so is there a difference in downloading something from the internet and installing a ‘Linux’ version of it, or installing that through a package manager?
Installing with a package manager is easier, since it handles stuff for you. You’ll usually only download software from your browser if it’s not available in your distro’s package manager.
Package managers may have multiple repositories, these are like lists of packages, and may differ from distro to distro.
A good analogy is thinking of a package repo (short for repository) as a library, and the package manager a librarian helping you search for a book.
‘use’ wine to run windows programs but what does that mean? Do I run it like a VM? But it’s not an emulator?
It’s a compatibility layer, to put it simply (since I’m not a WINE expert) it converts Windows stuff to Linux stuff, instead of straight up running a Windows VM.