Student or Learner
Why are you late?
How come your late?
The difference isn't between how and why, MsNyree, it's between how come and why.
how come is a shortened form of "How has it come to be that ... " and it simply means the same thing as why. It's just used in more informal situations.
Note that there is no S-V inversion in how come you are late? to mark it as a question. The inversion is understood to be in the ellided portion, underlined, above.