Originally Posted by Fingers
No difference. The bittering hops are added early in the boil and the finishing hops are added towards the end.
+1, what he said. Probably your "bittering" packet goes in the kettle with 60 minutes left to go on the boil. The other packet, labeled flavor/aroma will go in sometime in the last 15 minutes. Typically I think of flavor hops going into the kettle with 15 or 10 minutes left in the boil, aroma hops at something like 5, 3 or zero minutes. With a steep. Probably you are supposed to open the flavor/aroma packet and dump it in the kettle with X minutes left in the boil, then finish the boil, turn off the flame, put the lid on the kettle and steep for Y minutes, then start with the chiller.
Short hand for these hops additions is the number of minutes left in the boil in parens, so you might see in a quickly handwritten recipe (like one of mine ;-):
(60) Chinook, 13.8%, 21HBUs, 1.52ozs.
(15) Cascade 7.2%, 15HBUs, 2.08ozs.
or something like that. Actually I am n00b enough to work from printed recipes, but I handwrite what _really_ happened on the printout in real time.