Switch control both light and outlet
Typically A 1/2 Switched outlet is broken in the middle of the tab between the two screws. If the one outlet is always powered, there is constant power to that outlet and the other outlet is connected to the switch leg of the light switch.  If this is the case, then that outlet should already have a GFCI on it. If not, then you can replace the outlet with the GFCI but you want to be sure that the Switched 1/2 of the outlet is capped off, Taped and Labeled in the Box. 

Pictures are also Wonderful to see. (-;