they have similarities but ultimately I think they are completely different. therefore there is hairstylist and then there is cosmetologist, I think cosmetology has a wide range of things involved in it.
Cosmetology is more of hair and makeup, mani/pedi skills are included in this as well. Hairstylist is, well, they just do hair. You don't need to go to school to be a hairstylist. You go to school for cosmetology.