Howdy! It's your friendly neighborhood guild member here to help you sort this out.

First, I think my answers to similar questions here and here and here and here are going to give you the critical details you need, and most importantly, SOURCES.

The very brief answers to your questions (and, again: details and sources in the links) are:

How were medieval guilds organized? Were they ever divided by type?

They were indeed divided by type (merchant vs. trade craft) and then by specialty (using trade crafts, masons and carpenters and plasterers, etc.) and then by region (usually at the city level, but in rural regions perhaps a single mason's guild for a large but sparsely populated region) and then internally by rank (masters and journeymen and apprentices).

Were they just a collection of fraternities, or was there ever a governing body that managed them all? How did such an organization function, if it existed?

Was there EVER? Yes, eventually, kind of. Let's work backwards from today, right here in the good ole' US of A. If you're a union electrician, you belong to a Local union (that's your local guild hall, using medieval terms). That Local is part of a national union of electricians, within the USA. Generally speaking, if you want to move to...France, e.g., you can take your union card and use it as a cognac coaster--they won't care about your USA union membership (or, maybe more accurately but with the same result: they don't have to care about your USA union membership--they may choose to make things easy on you, but they don't have to). But that sort of national organization of guilds is really a product of the post-medieval world. I can't tell you for an absolute fact that there were no trade guilds organized at the national level in medieval Europe, but I can't recall ever reading about that, and (as is spelled out in a few of my other posts) that sort of organization would have been strongly contrary to the totally local level of guild organization that typifies medieval guild structure so...I would expect to have read a lot more about it if it had happened. (Disclaimer: I'm not an expert on merchant guilds, and I'm not an expert on guilds outside of the Western World, so I can't speak to those issues.)

And to nitpick very gently: I wouldn't call them fraternities. Fraternal organizations are, both connotatively and denotatively, at least facially charitable and meant for the public good. Medieval trade guilds DID serve a valuable public function by helping to ensure the competence of the people who built...well, everything, back in a time when government inspection of construction was binary: nonexistent, or totally corrupt. But the real purpose of trade guilds (and, to my limited understanding, merchant guilds as well) was to control competition in order to ensure stable and predictable prices for the benefit of the guild masters, who were usually owners of their own small businesses. So guilds were fraternal in just about exactly the same way that Standard Oil was fraternal.

I hope this helps, and if there's anything I've left out (between here and my linked answers), please let me know and I'll expand.