Honest question incoming.
While the end result may be very different, is there evidence that the root cause is different? I.e is it possible that FGM was started for an equivalent reason to male circumcision, and the way that female sexual sensation is affected wasn't the aim, but an unintended effect?
(I think others have explained this, but I'll a crack at it.)
Kinda, but it really depends on the culture practicing FGM. Unlike MC, FGM doesn't have religious roots, it's primarily a gender inequality problem.
Some African cultures uses FGM as a rite of womanhood, while others(middle eastern for example) used it to keep girls 'Pure' for their eventual marriages. In some societies, a virgin is highly prized and can potentially make or break marriage deals; FGM was their safeguard against a girl possibly screwing up her family's plan.
Hygienic reasons, as stated for MC, doesn't seem to be one of the reasons for FGM. Well, besides some weird old myths, like the clit impeding a baby's birth. There are no health benefits from FGM.
More info here:
http://www.who.int/mediacentre/factsheets/fs241/en/
Make no mistake, even though both practices have some similar roots(sexual control), modern implementation far separates them. MC these days is used for hygiene and cosmetic reasons, but FGM's sole intention is to control a woman's sexuality.
Edit: whoops, just noticed Funky's warning.