Wikipedia says, hard [r] is a trill, soft [rj] is usually a tap. I've tried pronouncing few sounds and that matches with what I feel).
Additionally [r] is postalveoral/palatal while [rj] is dental/alveoral.

You should be aware that some native russians are unable to pronounce [r] and [rj] saying [ʁ], [ɣ] or even [ʔ] instead. I've learned to pronounce trilled [r] only 5-6 years ago (having no problems with tap [rj] though). Used to say [ʁ] instead.