Impassive, stoic, phlegmatic, apathetic, stolid are comparable when they mean slightly if at all responsive to something that might be expected to excite emotion or interest or to produce a sensation.
The distinctions to be drawn between these adjectives hold true also of their corresponding nouns, impassivity or impassiveness, stoicism, phlegm, apathy, stolidity. One is impassive who feels or shows no emotion or sensation, without necessary implication of insusceptibility.
One is stoic who is indifferent to pleasure or pain; the word frequently suggests unflinching fortitude.
Phlegmatic implies a temperament or constitution in which emotion is hard to arouse or, when aroused, is moderate or restrained.
Apathetic usually implies either a remiss and culpable indifference or such a preoccupation with a particular depressing emotion (as care, grief, or despair) or bodily pain as makes one insensible to other emotion or pain and deficient in or devoid of the usual human interests.
Stolid implies heavy, dull, obtuse impassivity or apathy or utter blankness of countenance mirroring or suggesting such quality; often, specifically, it suggests impassive, mechanical, plodding, unquestioning, unresourceful adherence to routine.