well the differences are pretty easy... an interface is simply a way to get sound into a computer... and can be a single channel all the way up...
a mixer on the otherhand takes multiple inputs and combines them... now a mixer may have a myriad of other features... like EQ... compression... FX... and an interface???? yep... if you're thinking about a mixer with an interface built in there are some things you may want to consider.... if it's a usb design it mostlikely will only transfer the stereo mix to the computer... while the firewire types almost always do the individual tracks... also a $1k mixer aint gonna have the same convertors of a $1k interface.... so caveate emptor...