I believe the hand throttles mentioned above will no longer be type approved for new pedelecs onroad from sometime next year but of course that won't bar existing bikes
By definition a 'pedelec' only applies power when a sensor of some kind detects the cranks rotating. This is frequently combined with a hand throttle to vary the power provided (the usual crank rotation sensors are an on-off affair), but obviously won't allow the bike to start off on motor power alone, and the motor stops when the pedals stop turning. Pedelecs are an EU-wide definition.
Torque sensors detect how *hard* you're pedalling (so also qualify as 'pedelecs') and apply power in proportion to that. It feels more like a bicycle in a tailwind rather than a motorcycle, but these systems tend to be more expensive and sometimes need to be overriden to do the Right Thing when you change down to climb hills.
There are old British EAPC standards that bikes can comply to, which allow a hand throttle alone. Nobody build bikes to this spec, as the allowed power is lower (200W for an EAPC vs 250W for a pedelec solo bicycle) and you'd only be able to sell them in the UK, after type approval.
Leftpondians and other countries have a hodge-podge of regulations, many of which are extremely non-fussy about controls and power ratings. So there's a buoyant market in electric assist bikes and components that would be classed as non-road-legal motorcycles in the UK. Some Brits use this stuff legally off-road, or take the pragmatic view that you're unlikely to be prosecuted if you don't take the piss.