By declining an interview request, you are simply choosing not to interview with that particular company that sent you a request. By accepting an interview request, you are committing to an initial conversation with that company. Like any other interview process, if you decide you are no longer interested in that company, you can remove yourself from the interview process at any time.
A company that has sent you an interview request will know the status of only that request, not any other requests you have received from other companies.