I work for a private company with a little over 100 employees and we are working on July 4th but they are giving us July 6th off instead can they do this
and should the pay be different on a legal holiday?

Yes, they can require you to work on a holiday. They do not have to pay you any different. If you are non-exempt, you would have to be paid overtime, of course, if you worked over 40 hrs. in a week.

There is no requirement in any state that you be given any holidays off, unless you work for the government.

There are only two, possibly three, states that require premium pay for working on a holiday and Arizona is not one of them. Even the states that do have such a requirement, require it only of certain industries.