Linux is a type of unix based system. it's not unix but it's based off the same system.
That being said what you really mean is what's the difference between apache and IIS because the O/S doesn't directly handle web serving. Other components that work in the O/S do. eg: you can run IIS (web server) on a basic install of windows. you must first add IIS to the system)
If you use php/MySQL scripts mostly, it won't matter which you go with as functionality. But if your scripts use .htaccess files you will have to use an apache based server. 9 times out of 10 that means you're going to be working on a linux based machine.
If you want to use FrontPage extensions you can do that on Either Apache or IIS. Most companies hosting linux also have the frontpage extensions available.
The difference is much bigger if you have asp sites. Linux cannot run ASP natively like windows can. There are wrappers that some companies use to offer asp functionality, but it's crippled asp stuff and incomplete. the same is true using php on windows, but it's a much MUCH lower crippling problem. almost everything php will work on the windows installs.