Can I have two different GPU in my motherboard

Kind of, though it's not that simple.

Practically, on more modern versions of Windows, it'll 'just work' for most tasks.

For Windows 7, they need to be the same driver (so Nvidia only or AMD only). Windows 10 doesn't care.

I've run a third monitor on onboard video with some tweaks on Windows 8 and 10 with the primary monitors being on a separate video card, and that's roughly the worst case scenario. So yeah, you'd be able to drag programs between monitors, and what you're thinking of would be doable. I'd suggest cards of the same brand and roughly similar era (so an 800-1000 series) simply for driver compatibility.

With paired video cards, chances are your system will drop down to x8 PCIe lanes from x16, but there's little practical performance loss from this.

With some software, you can use a secondary/lesser card as a co-processor for specific tasks or simply pick one as a primary card. Photoshop specifically suggests using one card for your output, and to use identical video cards.

Adobe also says:

Photoshop currently doesn't take advantage of more than one graphics processor. Using two graphics cards does not enhance Photoshop's performance. Multiple graphics cards with conflicting drivers can cause problems with graphics-processor accelerated features in Photoshop.

So in this particular scenario, it's not that useful.

You might see some advantages with some CUDA or OpenCL loads but YMMV.

Yep, having two completely different GPUs in one PC is possible, as long as there are enough PCI slots. However, if you are planning to use SLI, it requires two of the same cards. Furthermore, you should remember not all applications take advantage of the dual GPU setup.

Source

I use a GTX1070/750ti with two monitors. I just had to make sure I set my display that the 750ti was plugged into as primary or desktop applications wouldn't use my 750ti.

I assumed that Chrome and such would use whichever GPU its window was on. Boy, was I wrong. My 750ti no takes care of gpu programs like chrome, twitch, bnet, and my games use my 1070. Noticed a 10-15 fps improvement.