The duration of the visa is determined by the embassy which had issued the Tourist Visa. If you have a 30 visa that visa will be valid for 30 days after entering Thailand. Hence the 60 day visa would be valid for 60 days after entering Thailand. That would be the duration of the tourist visa. See the rest of the post for more information about your Thailand visa and how this gets extended in Thailand.
Thailand Tourist Visa
Duration of extension for tourist visa :
The duration of the extension would depend if it is the first or the second. If you have as example been in Thailand for 55 days on a 60 day Thai tourist Visa, you may proceed to have the tourist visa extended for 30 days in country at Thai immigration. Once this has been granted you may extend the tourist visa again but only to a maximum of 10 days. There can be not further extensions to the visa unless there are other reasons. An example of this might be that you had suffered a heart attack and Thai immigration will extend your Thailand tourist visa on the bases of medical grounds.
Note that the cost of the visa extension is 1,900THB each time it is extended.
Note: Nationals from Bangladesh, China, India, Iran, Nepal, Nigeria, Pakistan, Sri-Lanka, Togo and Uganda may only extend for a further seven days.