Muay Thai has various stances which usually depend on which area you have been training in. Some "streams" prefer certain types of attacks such as punches to kicks and vice versa.
In instances like Muay Korat (North Eastern Style) which prefers the use of heavy punches, the boxer is standing more squared like a western style boxer as this gives more power to the punches.
Other Forms like Muay Ta Sao/Uttaradit have a long range preference and have a stance which has the boxer in a stance which is almost side ways like a fencer. The back leg is primed to be brought round at anytime to deliver quick succesive kicks.
Muay Chaiya has a more lowerd crouching like stance as its a much more defencive type of Muay. The stance is much more compact and can protect the boxer much easier than the other stances.
There are various other new types and older types of Muay Thai which differ from one another slightly in stances and kicks. Those who dont really know the small details about Muay Thai and only watch Muay Thai sport fighting wont see much difference. Many Western Kru's from what I've seen usually teach the more paralell stances because westerners prefer to punch a lot more than Thai people.
Hope this helps