same.
but the mannerism in which they do it is different.
when flashing at other males, they usually do that as a form of aggression. to show who is boss. they chase at the opposing wrasse and the fins are usually clamped down or open (depending on the wrasse. some wrasses flash with fins closed while some, open. it's species specific). this one does not last long at all.
there's also another type of flashing where the flashing or nuptial colours are exhibited, but the fish just cruises around the tank displaying it, without targetting anything in particular. this i think is to show the whole tank he's the boss. and to attract any potential females inside.
when flashing to females, they usually flash around the female. to attract attention. the flashing last longer, and there are pauses inbetween. flashing can even last up to an hour! occasionally they will barge at the female and chase them around the tank. when they do this, they swim very closely to the females as shown in the video i posted.
all these are just personal experiences i've encountered.
some fairy wrasses have more than one flashing colour. like cirrhilabrus condei, the condei fairy wrasse. it has 2 different flashing colours and no one knows why.