technically there shouldn't be reason why they both couldn't run on the same machine. They both are, at the end, just a processes running on a windows machine.
What needs to be realised is that both are web servers, so by default they both will be trying to run on port 80 (or 443 in case of https). Therefore at least one of them have to run on a different port.
And since you probably don't want to force users to type a port number into the URL, you would need to set up a reverse proxy server, that would handle the URLs, e.g. in a way that "http://myserver" goes to Connect and "http://myserver/gallery" goes to gallery. Or maybe 3rd domain could be better, like "http://gallery.myserver" and "http://connect.myserver".
Plus you need to have in mind that both Connect and Server have their own HW requirement, which you need to combine, otherwise they both will have not enough memory or CPU.
Basically, since Server and Connect are two different application and it is best practise to not run two different applications on one server, we recommend to use a dedicated machine for each of them.
Vojta T., PM for Data Connectors
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