As I go to test out my AVI to HDMI adapter I realize that my monitor cord is actually DVI. LOL. Whoops. (My other monitor is AVI) So I will return that and get a DVI to HDMI adapter. Now, I am looking at this. Will this do what I need it to do if I use a DVI to HDMI adapter? If not do you have any suggestions on what to buy to fulfill my wishes?
In general, again, this new device will handle switching video independent of OS.
The question is whether it will work with your video output types for both computers as well as with the video input on your monitor. I say that because the original way you stated your problem suggests that maybe you use a VGA input on your monitor. So, it might help if you provide the exact brand and models of both the Windows computer, the Chromebook, and your monitor. That will allow me to look up what video output formats your computers support as well as what video input format your monitor supports.
This goes back to the analog vs digital signals. VGA is analog only. HDMI is analog only. DVI can be either digital only, analog only, or both. The original device you were looking at was VGA only, which means analog only. This new device is HDMI only, which means digital only. If you need to "bridge" the analog to digital divide, then it will require a converter as just an adapter cable will not work. So, whether the original device or this newer device will work in terms of your video needs will depend on what your needs really are. And I do not really know your actual needs until you provide more info on your computers and monitor.
As to suggestions on what to buy, I don't generally offer suggestions on what specifically to buy unless I have used a product myself and know how well it works or not. In general, as I said before, it seems like you want a KVM switch. Once I know specifically what types of ports you have for your computers and monitor, then I can offer up an example of what would work for your needs. It will not be a suggestion on what specifically you should buy, but rather an example of what type of device you want to look for. You could buy that example, but I will typically be clear that I have not used that device, so I don't know how well it works. I typically mean it is an illustrative example of you want to look for so that you can then look at other options and pick one that you think would work for you pricewise as well as in terms of perceived quality (i.e. review rates on say Amazon).