In Latin, gremium meant the lap or bosom, and that provided us with a strange, but useful, term.
Gremial refers to a tight membership. The word started in academic circles, where it referred to a resident member of a university. That was appropriate, since the university was the Alma Mater (fostering mother).
Later, it was extended to any society or corporation, where it referred to full members, as opposed to honorary members. It was also applied to any bosom-buddy, any intimate friend.
Finally, gremial came to mean an ecclesiastical garment, an apron placed on a bishop’s lap when he was seated. Its purpose was to keep his costly vestments from being stained.
SIDEBAR: Asociacion Gremial de Auto-Taxi de Madrid
(substitute @ for AT above)