If I am military and I am stationed in South Carolina with a South Carolina license and a house but on my pay stub says Pennsylvania would I claim both states

It depends on your Home of Record. Where the military sends a service member for duty is not necessarily the "legal residence" or domicile. The duty is considered temporary, whereas the legal residence is more permanent.   

It sounds like you originally came from Pennsylvania.  This is where you will file your taxes.

However, if you do other work other than your military duties (work at the PX, do a paid job in town, or other non-service-related jobs) you will be taxed in South Carolina.

A person can change legal residence; however, it is important to understand that legal residence is established, not chosen. You cannot simply choose a state that is particularly friendly to military income and decide it is the legal residence; rather, citizens must first meet three requirements. The three requirements to change your state of legal residence are: 

you must be physically present in the state, 
you must intend to remain indefinitely in the state; and 
you must intend to abandon your previous legal residence.