Macs and Windows machines do have their own preferred file formats for internal hard drives, but external hard drives don’t always ship with these pre-installed. The hard drives should not be a problem, unless your computers are very old.
However, my Mac doesn’t recognise his hard drive, and his PC won’t recognise my hard drive.
I bought a 4TB hard drive for my dad, and thought it would be easy to copy the files over so he could use them on his PC. I have a Mac and an external hard drive that includes some important family files.