You know, I find it interesting about word-association, too, but in the true sense of the word, a motorized or motor-assisted bicycle is a "moped." While most of you are much older than me, and remember a true moped as something different, the word literally means "motor pedal". One definition I found is: (noun) "a motorized bicycle that has pedals in addition to a low-powered gasoline engine designed for low-speed operation".
Now, a
scooter is defined as:
(noun)
1. a child's vehicle that typically has two wheels with a low footboard between them, is steered by a handlebar, and is propelled by pushing one foot against the ground while resting the other on the footboard.
2. Also called motor scooter. a similar but larger and heavier vehicle for adults, having a saddlelike seat mounted on the footboard and being propelled by a motor.
When people call my bike a scooter, I quickly and firmly remind them of the above definitions, and make sure they understand it is NOT a scooter. Tom's right: scooters are just not nearly as cool as motored bikes!!