MTF means male to female. MTF crossdressing means male dress like female. MTF trans people means male to female transition, MTF trans people are female.
FTM means female to male. FTM crossdressing means female dress like male. FTM transgender people means female to male transition, FTM trans people are male.
The biggest difference from trans people and crossdressers is that crossdressers are still the gender they were born with, they just dress like the opposite gender. While, trans people are living as the opposite gender they were born with.