TAT is a branch of the government dedicated to tourism. It deals with licences and permits to legally commerce with tourism within and outside of Thailand. Any guide, travel agency, expedition group or tour operator needs to have some sort of authority to be able to do business in the tourism sector. The TAT logo and name are copyrighted and it is illegal for anyone to use the TAT logo and name on their product or services to underline the quality of their services to customers. The licence an entity receives, is approved by the TAT offices and it may be represented with a document, certificate or simply the licence number on the store or business card etc.
If you are being brought to a travel agency and they claim to be a TAT office they also claim to be part of the government. Thailand has numerous TAT legal offices and you can find the location on this link...
http://www.tourismthailand.org/about-tat-page/about-tat/tat-local-offices/
...if you think you were scammed, check the name of that travel agency and look it up in the list. If you can not find it, you were definitely scammed...
Here is a report on the TAT copyright infringement and why TAT copyrighted their logo and name.
http://www.thaitravelblogs.com/2011/08/tat-copyrights-its-logo-to-stop-travel-agencies-scamming-tourists/
Other names such as T.I.T, T.O.T etc do not exist in Thailand to represent some sort of tourism authority or licence