@Laura ****
you need to start answering questions that people are asking you in order to get the right answers (asking MORE questions before you give us the answers isn't gonna be all that helpful :( )
BE that as it may I'll try to answer the questions you've asked
IF your relative came into the country on a tourist VISA <- that they BOUGHT from a thai consulate before they came here and got stamped in for 60 days, they go to Chaengwattana to get their 30 day extension <- it will be issued on the spot and it will be added to the expiration date they have now
IF your relative came into the country without having bought any visa before they arrived and were stamped in for 45 days they go to Muang Thong Thani to get their 30 day extension <- itl will be issued on the spot and it will be added to the expiration date they have now.