A stimulant, or "upper," is simply a drug that increases alertness and awareness, or keeps you up. I do think MDMA belongs to this class, though I definitely don't put it in the same league as meth or cocaine.
The term "psychostimulant" more specifically describes stimulants that increase locomotor behavior in animals, and includes all the major dopaminergic stimulants such as cocaine, amphetamine, methamphetamine, methylphenidate. However, it does not include the milder uppers such as nicotine and caffeine. MDMA is considered to be a psychostimulant by many researchers, but that does not preclude recognition of its own unique qualities.