Pedelec
This refers refers to bikes that monitor your pedaling power output and add a certain percentage of motorised assistance. IE the Haibike mountain bike, you could select either 50%, 120%, 210% or 300% assistance. This means the motor will add up to three times the effort you put into pedaling.
Twist & Go
Until regulations changed in April 2015 and January 2016, Twist & Go eBikes were very popular. They use a throttle or on/off switch that gives power moving you up to 15 mph with no need to pedal. Although popular they are more like a motorised bike you can assist with pedaling, rather than a pedal bike that has a motor to assist you. The maximum non-pedaling speed is now 6 mph, which has seen a decline in popularity of Twist & Go eBikes.
Urban & commuter eBikes
These are made for getting around the town, making cycling on flat surfaces as roads and cycle paths as easy as possible. Sometimes city eBikes have smaller wheels, which makes it less of an effort for the motor to start them turning and is more efficient for stop start riding in the cities. Urban eBikes normally have a comfortable upright riding position and usually come with accessories like mudguards, stands, lights parcel rack.
Off Road MTB eBikes
The range of eMountain bikes pretty much reflects that of traditional MTBs. So you can pick up bikes with geometries and components suitable for cross country, downhill, freeride and enduro. Wheel size options include 26ers, 27.5ers and 29ers. You can alsohaven no suspension, hardtails, which is front suspension only, or full suspension. The components are the same as those used on traditional mountain bikes, so you can save money and get lower cost brakes, suspension and gears etc, or pay out for top of the range. eMTBs are somewhat heavier, but like the heavy downhill bikes this helps by providing more grip when cornering. They are also OK to ride on the road, but are less efficient on tarmac.
Hybrid eBikes
This is inbetween a mountain and urban eBike style. It can be a mountain bike frame with multipurpose tyres and front suspension.
Folding eBikes
Folding ebikes are a superb choice for commuters and economical for students and are incredibly convenient. Improved technology means they are now light enough to be very portable. Great if you lack storage space or cycle to a train station and then catch a train and finish the journey on two wheels.