QA Time!

Q: If a trans female told me "I identify myself as a female," what exactly does she mean by that?

Identify means to 'establish what someone is'. They are saying they identify as 'female'. This means if given the question, 'do you identify closer with male, female, non-binary, or other?', they would answer 'female'.

Q: Does she mean that she fits the female stereotype?

Part I: No. Gender identity and gender roles are entirely separate. It is her prerogative to choose a set of actions that make you believe she fits a female stereotype.

Part II: You may ask, 'ok, so how is a cis-male who identifies as feminine (but not female) any different?'... Well the difference is in how others perceive her; identity cannot be separated from how others perceive you... Ironically, you cannot have an identity without others to impart meaning on an identity through difference.

Q: Or does she mean she will feel more comfortable with a female body?

More than likely. She probably has/had gender dysphoria/euphoria. This can arise from several physical factors; factors that range from phantom limb sensations for missing boobs (as many people born without limbs have as well) to the incorrect pheromone recognition. The brain has a signal for 'wrong/mismatch' and dysphoria/euphoria could come from similar 'wrong/mismatch' signals.

Q: And if it is about the body, is it out of mere preference? Or does she have a "female brain" that somehow doesn't fit a male body?

Part I: Physical gender is composed of many 'traits'. These include chromosomes, structural differences in the brain, pheromone production, hormone levels, physical appearance, et al. The brain is very capable of knowing when any of these traits don't match it's internal perception (which is developed separately from the 'traits' themselves).

Part II: The relationship for a mtf transgender individual on brain-structure when compared with a cis-female is complicated; but absolutely undeniably related. mtf transgender individuals experience a distribution change in neural connectivity that places them within female standards. This is an ongoing research field.