DAF cars (i.e. Type 600, year 1958-63) were the first to use a CVT automatic (they had a double cvt, 2 belts etc.).
There are many kinds of automatic:
Full automatic (nothing to do for the rider),
semi automatic (rider changes only gear, cluth is automatic; i.e. Honda Super Cub, with more than 60 million bikes the top-selling vehicle of the world),
automatic with torque converter (i.e. Honda DN-01), CVT (most scooters), CVT & gears (Burgman 650), ...