I researched it after I posted. 'Dissertation' is the AE equivalent to the BE 'thesis'. However, they are interchangeable due to the AE/BE nonsense of 'boot/trunk' and 'bonnet/hood' etc.

That said, if a Brit was aiming for a doctorate, he would likely use 'dissertation' rather than 'thesis', but an American would use 'dissertation' regardless of whether he/she was studying for a masters or PhD.

Quite frankly, who cares?