What is the Connection Between Space Marine Chapter Organization and Actual Armies?

[ElectricPaladin]

I'm working on the background for my Blood Ravens force, and I've suddenly realized that I have no idea how this actually works. I know that you have the chapter, that within the chapter you have the ten companies overseen by the leadership, the librarians, and the armory. What I don't understand is where in this structure you find the random collections of models fielded by the average player.

Do space marine captains (or librarians, or whatever) run around with detachments drawn willy-nilly from the ten companies? Should I imagine captain wandering around space with his own strike cruiser, his own tanks, and so on, looking for trouble? Should the characters my army have ongoing relationships (ie. my sternguard vets have a rivalry with my terminators, or my scout sergeant has a deep man-crush on my captain, or my librarian, apothecary, techmarine, and captain have some kind of "bridge crew" friendship dynamic). Or should I imagine that the army list I bring to a given game is merely the force assembled by the chapter master to deal with a specific threat (ie. my opponent's army)?

I'm looking forward to reading your answers. Thanks for clearing this up for me.