Moped:- Motor and Pedals, as simple as that. A pretty well universally used term.
Mokick:- Motor and Kickstart, used to differentiate between pedal start and kick start types. This term is used widely in the USA. In the UK we don’t use this term but call all 50s, mopeds even though mopeds haven’t needed pedals here since 1977.
Mofa:- from German Motorisiertes Fahrrad (motorised bicycle). Originally meant a very low powered, restricted moped in Germany but is widely used there and in the Czech Republic and Slovakia to mean any moped.
Autocycle:- In the pioneering days of motor cycling the term “autocycle” meant any powered two-wheeler and was, therefore, synonymous with motor cycle. Between the two World Wars a utilitarian style of motorcycle with pedals and a small engine, of between 75cc and 100cc capacity with single speed transmission, was developed and are now what we generally call autocycles.
The term autocycle has also been applied to other types of machine at various times. Bicycles powered by auxiliary engines became popular after World War II; these were initially classified as autocycles until the term “cyclemotor” was applied to them. Later, purpose built under-50cc machines were described as “light autocycles” until the word “moped” was imported from Germany in the mid 1950s. Neither of these types is now thought of as being an autocycle.