In the RAF Club is a display of many squadron crests. Definitions of crest on the Web: (heraldry) in medieval times, an emblem used to decorate a helmet.
Since the badge is created by the college of heralds I submit that the framed and signed artwork is a crest.
When worn on a grow bag it is a badge: Definitions of badge on the Web:
an emblem (a small piece of plastic or cloth or metal) that signifies your status (rank or membership or affiliation etc.); "they checked everyone's badge before letting them in"
any feature that is regarded as a sign of status (a particular power or quality or rank); "wearing a tie was regarded as a badge of respectability"
The RAF Marham web site, the de facto online source for unit crests etc is:
RAF SQUADRON CRESTS, RAF STATION CRESTS, RAF UNIT CRESTS AND BADGES
RAF MARHAM CRESTS GALLERY INDEX
So there