Brads are usually 18 gauge while finish nailers use either 15 or 16 gauge nails.
Basically, brads are great for doing small and fine wordworking stuff (cabinet making, picture frames...somewhere the stresses will be less). Finishing nails are heavier and typically longer 2.5" vs. 2" and will hold more weight.
Just to confuse things, 15 & 16 gauge finishing nails are called "brads" by some manufacturers. If you check out the nail gun literature, you'll find they recommend finishing nails for trim, door jambs, floor molding, crown molding, chair rails and most anything you'll be doing inside your house.
Check out the Paslode nailers, high neat quotient and they work great...and no compressors. Got a new 250 Finish Nailer on Ebay for $235 so you can get good prices and then sell it when you're done for what you paid for it. Good luck, measure twice, cut once, swear and then cut it correctly the second time.