In the Catholic tradition, St. Francis was supposed to have found 3 orders. The First Order, the Friar Minors was founded in 1209. The Second Order, the Poor Clares (known as the Poor Ladies then) was founded in 1212, when St. Clare convinced St. Francis to allow her to follow his devotion. Finally, in 1221, the Third Order, the Brothers and Sisters of Penance was founded for those who, because of duties and responsibilites in the world, could not follow fully St. Francis' Rule.
In general, anyone who professes to follow the Rule of St. Francis of Assisi could be called a Franciscan. The Rule most notably forbids the Franciscan from accepting money either directly, or through an intermediary.
Famous Franciscans include St. Francis and St. Clare of course, but also John Duns Scotus, Maximilian Kolbe, and Padre Pio. Dante Alighieri and Christopher Columbus were also Franciscans, members of the Third Order of Penance.
Finally, I should mention that there is an Anglican counterpart of the Franciscan order, the Society of St. Francis.
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