Why do some Priest wear the cassock or black shirt and pants, while some wear the brown monk type robe?
Depends on their priestly order.
Depends on the Order. Franciscans wear the brown, long robe. Other orders have light grey robes, white with a cowl, etc. Diocesan priests (non-religious, often in parishes) you are most likely to see in black slacks and black shirt with collar and a cardigan sweater. Jesuits used to always be in the long black cassocks, now probably shorts and a sport shirt!