the term 'slingshot' actually refers to the slide design of the mikuni carbs - if you've ever looked at the shape of the slides from top down, they're flat on the airbox side, and have a semicircular middle part on the engine side. so they look kinda like a slingshot.
all of the carbed gsxr's from the 2nd generation on (including the srad's, i believe) came with mikuni carbs with the 'slingshot' slide design, of one size or another.
but i think only the 88-89 (maybe 90 as well) 750 gsxr's (and 89-90 1100's) actually have the word 'slingshot' somewhere on the fairings, and that's what led people to start calling those bikes 'slingshots'.
so in much the same way that people call the 96-99 generation gsxr750's 'srads' (like i just did
) even though 'srad' is not the name suzuki gave to those bikes but rather a name for one particular feature of those bikes that happened to be written on the fairings, people tend to call the 88-90 generation gsxr's 'slingshots'.