Some routers now give you the option of hosting two separate SSID's, though I am not aware of any that let you use separate channels for each SSID. (If there were, they'd probably be more expensive than just buying two cheap routers anyway!)
Routers that can host two different SSID's typically let you decide how you want these two "networks" to interact. They typically have web-based configuration panels that let you control the level of interaction between SSID's. You can completely firewall off the two networks from eachother, or let them fully interact.
I was able to setup completely different encryption schemes for each SSID on my Netgear N300 router (WNR2000v3), though I was -not- able to select different channels for each one - they share the same channel.
Wireless devices consider the SSID as the unique identifier for a network. If you have two different SSID's, your device assumes that each one is for a separate network. On the other hand, if you have one SSID at home, and find that same SSID somewhere else, your device will consider these two hotspots THE SAME, and can not differentiate between them.
You CAN NOT have different encryption settings for two different routers that use a common SSID, and connect to both of them with one device - unless you manually intervene. This might change as more and more devices come to contain GPS units - it is conceivable that SSID + location might eventually become a differentiator.