Being transgender is when someone identifies with a gender that they were not assigned at birth. Trans women are women and trans men are men they just weren’t recognized as such when they were born.
MtF and FtM are a bit outdated nowadays. Technically, they do mean the same thing as trans women and trans men but there’s an implication that you once really were the gender you were assigned at birth and then identified as other later in life and a lot of people don’t like that so try not to use that about someone else unless they said it about themselves.
Hopefully this helps! Don’t be embarrassed to ask more questions or hmu off anon if you need to c: