As a native English speaker, my opinion is that they are slightly different in connotation.
"I am first" seems more like a temporary thing like "I'm first in line," or "I get first pick." Basically, "I'm first today" or almost "I'm next."
"I am the first" seems more stressed, like "I am the very first ever." In a situation where no one has ever done that before.
If I were at a bank and there were several people there but no clear line and the teller asked, "who is first?" I would never answer with "I am the first." I would answer with "I am first" or, more likely, "I'm first."
"I am the first" is more likely the answer to the question, "how many people have done this before you?"
Oh yes, there is a very distinct difference.
"I'm" is one syllable. If I were to try to spell it in Turkish it would probably look like "aym"
"I am" is two syllables. I'm not sure how I would spell it in Turkish. When you say it like you would in normal speech (as opposed to when speaking to be super clear and separating all words out) it's a bit like "ayem."
lılacfrogs ıs correct... they are definitely not the same.
"I am the first" is indefinite and absolute. I am the first... son of my mother. I am the first man to climb mount everest. No one can ever replace me being that.
"I am first" is relative and circumstantial. There is also a difference in grammatical English between writing the word first and using the number 1st
generally 1st 2nd 3rd is positional compared to other ordinal sequences
First, second, third is specifying facts or figures etc.