Yamaha FS1's, Suzuki A50P's and Kawasaki AE/AR50's are all manual mopeds with a manual clutch.
All FS1's are 4 speed, and suzuki A50P's are 5 speed.
In the UK, anything witha 50cc or lower engine is a moped, gears or no gears.
C50's etc have a semi automatic clutch and are known as 'crunchies' for a good reason.
Keep on riding!