There are many mentions of the "12 tribes" (e.g., the tag of this question). But there really were 13: Ya'akov had 12 sons, of which each was the ancestor of one tribe except Yosef that was the ancestor of 2.
I know that there were 12 tribal territories because Levi had no land of its own. But on the other hand, Levi had its own symbol while Yosef only had one symbol (see question and picture). But AFAIK nobody ever mentions a "Yosef tribe".
So what 12 tribes are usually meant?
As you note in the question, sometimes Levi is excluded (and Yosef split up) and sometimes Levi is included (as is Yosef). Thus, there are two divisions into twelve tribes each. Other examples — you mention the divvying up of the land and the tribal symbols — are the post-exodus desert travels (which was by tribe, with Yosef split and with Levi excluded from the configuration) and the blessings of Yaakov and Moshe (at the ends of Genesis and Deuteronomy, respectively, where Yosef was not split and Levi was included). I can't think of any situation in which all thirteen potential tribes (including Levi, Efrayim, and M'nashe) are included simultaneously. This explains the common reference to "twelve tribes". So your question "what 12 tribes are usually meant?" has, I think, no answer: either of the two possibilities, depending on context.
