Yes, private unaided schools show variation in salaries they pay to the teachers. The salaries of those unaided schools are fixed by the particular institutions basing on the funds they develop. The variation of salaries only depends upon the economic standards of the institute. However there are some schools don't pay genuinely. Supreme Court has also announced that "teachers of unaided schools cannot claim a salary equal to what is being paid to govt teachers." This is said because the allowances and the salaries of those private teachers is a contract between teacher and the institute and is not within public law.
But for the govt and aided schools 6th pay commission is applicable, where they are paid according to govt rules.