Gatherings ~ sections ~ signatures ~ quires ~ bundles ~ segment ~ chapter ~ fragment ~ component ~ are all more or less synonymous. Unfortunately some of these words also have separate ~ dissimilar ~ meanings.
This needs some explanation. I may be wrong over some statements ~ please write and correct me if your authority is more knowledgeable than mine ~ my bloggy notes are as one hobbyist to another hobbyist. Bookbinding is fun ~ do not let pedanticism spoil it ~ do not let the theory spoil the practical.
Codex binding involves gathering some folios into a sections and then binding them into a book. Sections are sometimes called quires and are widely known as signatures in the USA and amongst a great many other users. It is not wrong to say 'signatures' but I was taught that signatures are the printing marks ~ unique to each section ~ that enable the binder to collate the gatherings correctly [126816]. To me that leads to entirely different things ~ so I avoid confusion by not using 'signature' for 'section'.