My medical certificate was 100B, the residence certificate was free (took 25 minutes) and I was 75 minutes at the DLT to get my first 2 year licence for 205B. This was Sa Kaeo province.
Embassies come under the Ministry of Foreign Affairs and Immigration comes under the Ministry of the Interior so they are completely separate. Both issue Visas (but not necessarily the same Visas) but only Immigration issue Extensions of Stay.
If you don't have the required numbers of days remaining and you are indeed still on your Visa (or Visa Exempt) 60 day entry stamp you can get a 30 day extension at Immigration.