In most fields I'm familiar with, first authorship is for the lead author. But I've heard that it wasn't the case in some fields. Is that true?
In different fields, the order in which authors are listed may be interpreted differently, that is true. In some (math, CS) authors are generally listed alphabetically, so you can't conclude anything from the order. In some fields the final author listed is the head of the lab in which the work was done. This person may be responsible for a lot or a little of the actual contributions.
In some fields the first author listed is understood to be the one that did the majority of the work, but in some of those fields the first author listed is also just assumed to be riding on the coattails of the last (supervisor) author.
It is very complicated. In some fields people fight over the ordering very bitterly and many questions come here for "resolution", which we can't provide.
In some fields, sole authorship of work derived from doctoral studies is the norm and others who help get acknowledged, but are not co-authors.
There have been a few papers, in the sciences, in which the list of authors is longer than the paper itself. I think there was one case where there were so many authors that it ran afoul of the journal's page limit. Imagine how many people contribute to major work at CERN, for example.