You might be thinking of brown dwarfs. Red dwarfs are fully qualified stars which sustain nuclear fusion in their cores. Brown dwarfs do not, though still emit radiation by other various means.

Jupiter is also somewhat close, in astronomical terms, to being a brown dwarf. It is not even remotely near being a red dwarf.

Your last point is correct though. Red dwarfs last much, much longer than all other stars due to being fully convective which allows them to consume all their fuel uniformly.