client server design

Say, for instance, that I have a client and server engine architechure following something along the lines of enguity: p2. Lets say, just to keep everyone into splitting the two apart, that the server handles collisions and the client handles rendering. From here i load a terrain or a level of some sort. Does this mean, assuming that collision data is about every polygon incorporated, that i must have two sets of the same exact data on both the client and server? Duh. But what about when this is a local game, and the client and server are merly connected via some pointer ( in an abstract sense ). This is where i am confused. Do I have two sets of the same level data, one for collision, one for rendering(?) while keeping the same client server architechure in a local scope? Thanks. andy