If you mean the conjugation of "hairu"(enter), it should be "haitte," not "haite." The other possibility is, "kite" is conjugation(-te form) of "kiru" , and "haite" is conjugation of "haku"(wear). "Kiru" is used for wearing clothes such as coat, shirt, dress, suits, sweater, jacket. "Haku" is used for wearing bottom clothes such as pants, skirt, socks, shoes.

They are all jussive,but the former is collocated with the place where the speaker want the lister to come. The latter is collocated with the space where the speaker want the lister to enter.

Kite is a conjugation of Kuru, which means "to come". Haite is a conjugation of Hairu, which means "to enter" or "to insert"