I received a ticket when on holiday in usa for running a red light, but was home before my court date, does this ticket only apply to the state I was in or will I be held if I arrive in a different state next time I vist, or will I be OK to get into usa

If they care enough about your non-appearance to issue a warrant it will show up in every State as well as a the border when you try to get back in.

My sister got a ticket in Ohio, didn't bother appearing and couldn't renew her drivers license in NYS.

Yeah the Department of Transportation is a nationwide thing now so you can't get away with anything from one state to another. So you would need to take care of it.

If you can possibly pay just a fine, pay it as soon as possible. If you miss your court date you will have a warrant out for you here in the states. Warrants here in the states do not go away ever. Better to pay the fine versus having a non expiring warrant on your head.