@Jeanette *******
, you are mixing up some things. You cannot apply for any extension outside Thailand. You could apply for a tourist (or other) visa before you travel to Thailand. Those are totally different things.
Single Entry Tourist Visa from Thai embassy gives you 60 days stamp upon your entry to Thailand. In comparison, visa-exempt (visa-free) entry gives you 30 days.
30-day extension at the local immigration office adds 30 days to your entry stamp based on tourism (SETV or visa-exempt) once.