The term Franciscan is used to refer to the Roman Catholic religious orders which follow the rule of St. Francis. The best known group, the Order of Friars Minor (commonly called simply Franciscans) is a mendicant religious order of men tracing their origin to Francis of Assisi and following the Rule of St. Francis. The official Latin name is the Ordo Fratrum Minorum (literally, "Order of Little Brothers"); Francis thus referred to his followers as "Fraticelli",[citation needed] meaning "Little Brothers". Franciscan brothers are informally called friars. The order has historically been known as the greyfriars. The modern organization of the Friars Minor now comprises three separate branches: the 'Friars Minor of the Leonine Union' (OFM); the 'Friars Minor Conventuals' (OFM Conv), and the 'Friars Minor Capuchins' (OFM Cap). The Friars Minor were constituted officially in 1517 and the Capuchins in 1619.
The visiting priest, if wearing the brown robe, is a member of a Franciscan order. And, sure, a priest from a different order may visit the Church.
FYI - Sean Cardinal O'Malley, is a Conventual Franciscan.
Also, there is a 3rd Order of Franciscans, comprised of lay people who ascribe to follow in the footsteps of St. Francis. This is - The Secular Franciscan Order.