Short answers, pulled from the story.
The Roman assemblies began as meetings of the Roman people convened by a magistrate during the regal period. These early gatherings focused on electing the Roman monarch, though historical records from that era remain sparse and poorly documented.
After the traditional date for the overthrow of the monarchy in 509 BC, the centuriate assembly took on the role of electing consuls while the tribal assembly emerged shortly after the republic was created. Citizens voted directly within specific blocks rather than casting individual ballots, where a majority of these blocks determined the final decision without representatives.
Three distinct types of voting blocks existed: curiae, centuriae, and tribus, which gave rise to the curiate, centuriate, and tribal assemblies respectively. Before any voting could occur, notice had to be given to citizens and the presiding magistrate took auspices from the gods to ensure divine approval before calling the people to vote.
As the empire grew, emperors seized direct legislative power, causing the assemblies' importance to fade rapidly until they became entirely obsolete by the third century AD. During the middle and late republics, only the centuriate and tribal assemblies held significant political relevance despite holding broad powers under specific conditions.
A comitia was an assembly summoned specifically to make decisions about elections, laws, war, or guilt while nothing was enacted during a contio meeting as it existed purely for public address. The word concilium referred to some kinds of assemblies including foreign ones and meetings of the plebeians at Rome with usage being rare in Latin.