Will you believe me if I repeat the affirmation a third time?
You did refer to a "double-8 projector" which doesn't really exist.
OP, there was no need to refer to Standard (or Regular, in American) 8 as anything other that just 8mm until Super-8 came along. So Standard-8 is sometimes still referred to as 8mm. Super-8 never is. All the two have in common is the width of the film- frame size, perf size and pitch, and even where the perf is in relation to the frame are all different. In 8mm, it's on the frameline, like 16mm; in S-8, it's halfway down the frame. This protects the perf when the film is edited- you don't have to cut the perf in half.
8mm. perfs are the same size as on 16mm, but half the pitch. I have viewed slit 8mm. on my Steenbeck very, very carefully- you get two frames at a time.
There are some dual-gauge projectors but the engineering is a bit of a fudge so they're not recommended.