Not being Catholic, I just assumed St Francis was a priest. How does a brother differ from a priest? What are the criteria for being either?
One who is simply a brother -- a member of a religious order like the Franciscans, Dominicans, etc. -- takes vows of poverty, chastity, and obedience, but has not been ordained a priest and cannot celebrate Mass or confer the sacraments.
A priest can be either a member of a religious order (and take the same vows), or can be a diocesan priest, reporting to a bishop (in which case he takes vows of chastity and obedience).
A priest in a religious order is also a brother (yes -- a father and a brother at the same time!). Priests and brothers who belong to religious orders live in "community," that is, in friaries, monasteries, or abbeys.
What is the criteria for being either? (I assume you mean why would you be a brother who's not a priest). It depends on which one the Lord is calling you to. A lot of discernment with spiritual directors is necessary to distinguish between the two, in some cases.