Differences in the Catholic Religious Orders?

[Bluebright]

Actually, Carmelites can be active too, their charism is community, prayer and service. You are thinking of cloistered nuns, which their most certainly are in the Carmelite order as in others, but there are also active Carmelite nuns as well as a wide variety of lay Carmelites, who are seldom, health permitting not active in some way.
But I understand your plight, it is tricky to summarise the orders, well done on attempting such a tricky task! Don’t mind the minor corrections, you are merely providing more information for the person who posted initially

 

[Vico]

So I’m really interested in all the Catholic religious orders. …

• Institutes of Consecrated Life - religious institute (make public vows, live in a community; orders and congregations)
• Institutes of Consecrated Life - secular institute (make public vows, live in the world)
• Societies of Apostolic Life (originally called societies of common life) - (do not make public vows)

http://www.catholic-hierarchy.org/country/xrel.html