There are different types of Studio Monitors.
The ones used in a Pro Studio would usually incorporate some if not all of the following:
- adjustments for near field listening environments because the speakers are usually on a mixing desk very close to the recording engineer
- protection circuits for drivers - especially in live recordings when you might overload things (positive feedback when mics get too close to speakers or someone drops the mic etc)
- active amplification to match to studio desks
Of course there are some "consumer" or home speakers marketed as studio monitors but that's more marketing.
The weird thing is that it isn't always true that studio monitors monitor have a flat frequency response
I think there was a mag review I read many years ago that measured the more popular pro monitor speakers vs consumer ones and it turned out a lot of pro speakers were far from flat. Sometimes they are tuned to work in a type of environment like a computer desk etc.