LLCs are partnerships for tax purposes in the US (unless they have only a single owner, in which case they are disregarded), hybrid entities for legal purposes in the US however many owners they have, and are either corporations or partnerships outside the US depending on the country. Most countries treat LLCs as corporate-type entities regardless of the number of owners, and only a handful will treat an LLC as a disregarded entity if it has a single owner.
Nope, still more complicated than that. Single member LLCs are not partnerships by default. Multimember LLCs are partnerships by default. Either group can choose to be a yet a different category. See citation and quote in https://news.ycombinator.com/item?id=16961968 .
You're right, I left out that single member LLCs are disregarded entities because I wasn't trying to be comprehensive. I've updated the comment with more detail.
[1] Edited to be more comprehensive.