Jason瘋英文 :回首頁

Depending on context they could have the same or slightly different meanings

I have finished

would be said after completing a task either very recently or some time in the recent past

I am finished

would be said after very recently completing a task.

It can also have the meaning of hopelessness as a person faces impending doom

I've lost everything, I'm finished.

or drawing a dramatic end to a relationship

She said she was finished with her boyfriend.