There's several different ways to use multiple monitors. The most common is extended desktop, which h windows treats as 1 very long desktop, but still retains primary and secondary for actual Windows themselves. Like having 1 desktop but split into 2. The other common way is through use of amd eyefinity or nvidia surround but they pretty much require identical monitors, since it's considered truly 1 desktop, no splits.
I'm running a 1920x1080 primary and a 1024x768 secondary on 2 different pc's, no issues. Just requires a little setup adjustment in control panel to set primary and secondary monitors with their respective resolutions.