message
Wphew, man, I don't know if I ever knew the answer to that.
The '57s and '58s (I had one of each) were 4-speeds. Just before or just after the 1300 cc Guilietta morphed into the 1600 cc Guilia (1962), they changed to a 5-speed.
I don't know who made them.
Here's a deep-trivia bit for your collection. You can tell a '57 or earlier Guilietta from a '58 or later by the distributor drive gear. The earlier ones were bronze, and usually worn out, and the later ones are steel.
I put the engine from my '58 into my '57, and then swapped *that* out for a used Tom O'Brien Veloce race engine.