To add to dewey's feedback (just piling on, not any different that what he says, just another example): You can have as many networks as you want. You route stuff via gateways/masks/etc. (via routes, but if you set it up right those get done for you). Where traffic goes, based on the destination and how that masks in the route (network/address/mask) will go through a gateway if defined, or else directly on the network (to dest), or if it doesn't match it goes though a 'default' route.
So for example, you can have like:
Router:
- IP 10.0.0.1
- Network 10.0.0.0
- Netmask: 255.255.0.0 (or 255.255.255.0)
Others on the network would be like:
PC A:
- Net1:
-- IP 10.0.0.2
-- Mask 255.255.0.0
-- Gateway 10.0.0.1
- Net2:
-- IP: 10.1.0.2
-- Mask 255.255.0.0
-- Gateway none
Other PCs same (with different IPs on same nets of course).
Your default route would be 10.0.0.1 (your gateway, or router IP).
So let's say you go to connect/copy/etc. to a share or service on 10.1.0.3 from 10.1.0.2 (your 10g), the dest is going to match your 10g network 10.1.0.0 mask 255.255.0.0 (i.e., 10.1.x.x), so routes that directly to 10.1.0.3 via the interface on that network 10.1.0.2 (your 10g).
If connecting to your router, or something else on your router network, it sees it needs to go on the 10.0.x.x network, i.e. out your 10.0.0.2 or 10.0.0.3.
To "some other" network (e.g., internet), the dest IP/mask doesn't match your local networks, so will route via the interface/gateway defined by your default route (in this example, over 10.0.0.2 or 10.0.0.3 interface to the dest IP, via gateway 10.0.0.1 - your router).
That's basically what it would do. Of course, you have more fine tuned control over any aspect of your network topography.
I did it for a while years ago using a linux server, where I had 3 ethernet cards, 1 to the router, 1 to home network, 1 to private servers I wanted off my home network (I was also doing a double nat, but that's another story).
Bottom line is, as dewey pointed it out - no problem.
Keep in mind your networks can't be physically wired together (10g & 1g) without everything going through smart switch(es), so you would need two physical typical switches with individual cables for the PC connections.
htw