To pretend they are different is a clear case of denial.
"Faggot" means gay person in exactly the same way "nigger" means black person.
Faggot is used as an insult, and gay people are offended when a person in seriousness uses that word as an insult.
Gays and straights alike are offended when called a 'faggot' by someone they don't like.
The two terms are both, clearly, gonna get you into a fight if you aren't careful where, when and how you use them.
Maybe where you are from but not here.