Derives from the scene in The Blues Brothers in which the eponymous band cruise into a cowboy bar and claim to be the act that's actually booked their, stealing their gig. As they're setting up, they try to get an idea of what they should play:
Elwood: What kind of music do you usually have here?
Bar Manager: Oh, we got both kinds. We got country and western.
Can also be used for the inversion, where an insider who really knows the diversity of a field winces at what a dabbler considers "diverse":
Grognard: "What kind of games do you usually play here?"
WoW Refugee: "Oh, we play both kinds: Dungeons and Dragons."
addendum, 16 Feb 2010: "I don't play D&D, I play Pathfinder."
In rare instances, it works both ways simultaneously:
Customer: "What kind of comics do you sell?"
Loyal Diamond Minion: "Both kinds: Marvel and DC."