Out and about with my Fanny.

[sexobon]

In that instance, the terminology is a close match. If your rainfly/flysheet has an attached projection that can be extended out to form a roof beyond the tent entrance, we'd call it an awning. If it additionally has walls, then a vestibule.

In military slang, a British basha is like an American poncho hooch. Both work as tarpaulins having grommets along the edges for suspension lines. US military ponchos are dual purpose having the edge grommets and a head hole with hood which can be tied closed in tarp mode. It also has snaps to create sleeves in poncho mode. The basha is a basic tarp.