The comitia tributa, the tribal assembly, was made up of spokesmen for the 'new' tribes, as initially defined by king Servius Tullius. If the king had originally created 20 tribes, then this was expanded to 35, of which four remained the tribes of the city of Rome (four 'new' tribes:sucusana, esquilina, collina, palatina).
It elected the lower magistrates (curule aediles, quaestors) and other officials. In the later republic became the chief law making body, together with the concilium plebis.
The concilium plebis, was the plebeian assembly. It could only be summoned by the Tribunes of the People (tribuni plebis). It was made up in the same was as the comitia tributa, but with the exception that the upper classes were excluded, hence only allowing admission to plebeians.
If at first the assembly could only pass laws (plebiscita) which would affect the plebeians, then from 287 BC onwards its decrees became effective for all Romans, irrespective of class. The assembly also elected the tribunes and plebeian aediles.
In the later republic became the chief law making body, together with the comitia tributa.