yes, peanut is used in the US while groundnut is a british term, both refer to the seed pod of the Arachis hypogaea. But be aware that another group of north american plant Apios spp. is also refered to as "groundnut" but these are tubers and not the seed pods of the "tor tow" that we eat
not many people realise that it is actually a legume, and has the strange habit of the flower plonking onto the ground and the "fruit" or seed pod growing into the ground now you know why the chinese name for it is "hua shen" literally "grown from flowers". checkout the pics here.