Prior to Francis, the last pope we had from a religious order (as opposed to a career diocesan) was Gregory XVI in 1831. Now we've had two religious popes in a row --- Francis, a Jesuit, and then Leo, an Augustinian.
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Diocesan priests “work” for the bishop in a particular geographical area and are in the “corporate” hierarchy of the church.
Religious orders are sort of independent from the the church hierarchy and report through to the leader of their order, at a global level. They often focus on specific things and may have different vows. Franciscans are known for their work with the poor and personal vows of poverty, for example. Also the order is a community that has its own governance.
I have friends who are in a similar organization as nuns. They govern themselves democratically and globally. It’s pretty amazing - we helped them setup their real-time voting system to manage their community. Each group is different.