Can I just carry my national driving permit?
If you are not a resident (i.e. you are on a tourist visa or exemption of visa), you only need your national driving permit to be able to drive in Thailand. So, if you are visiting Thailand as a tourist and you want to rent a car for just a few days, you just need to carry the driving permit you obtained in your home country. This is clearly indicated in the Motor Vehicle Act:
In case there’s a treaty between the Thai government and a foreign government regarding mutual acceptance of driver’s license, an alien who doesn’t have an immigrant visa may drive a motor vehicle with a driver’s license issued by such a foreign government, or an automobile association authorized by such a foreign government.
Do I need to get an international driving license?
An international driving permit (IDP) can be obtained in your home country. Basically, it is a translation in English of your original driving license, so if your national driving license is not in English, it can save some hassle with the police if you can produce an IDP.
Be careful of the period of validity of your IDP, as it can be as short as three months, no longer than three years in any case, and no longer than the period of validity of your national permit. Besides, to be valid, the IDP must be carried together with the national permit.
In any case, to determine if you need an IDP or not, you should also read in details what any contract says, for instance your travel insurance or any vehicle rental agreements.
Who needs a Thai driving license?
People who are residents in Thailand (on a non-immigrant visa) are required to obtain a Thai driving license in order to legally drive a car or a motorbike.
Further reading: How to obtain a Thai driving license?