But what needs to be considered here? And what makes the difference?

Pedelec:
With a pedelec (pedal electric cycle), cyclists still have to pedal themselves. The bike is supported by an electric motor with a maximum output of 250 watts. Some models have an additional starting and pushing aid of up to 6 km/h, which is particularly helpful on hills. While cycling, the electric motor can reach a speed of up to 25 km/h. However, even higher speeds can be achieved with your own effort.
In legal terms, the pedelec is treated the same as a "normal" bicycle. No insurance license plate, registration or driving license are required. Furthermore, there is no obligation to wear a helmet or any age restriction.

S-pedelec:
Due to a maximum power of up to 4000 watts and pedal assistance, speeds of up to 45 km/h can be reached on the S-pedelec.

A little bit of background information:
Special legal regulations apply to S-pedelecs, as they are no longer legally a bicycle, but a moped. There is therefore a helmet, insurance and driving license requirement (class A, M). The minimum age is 16 years. 
In principle, the S-Pedelec belongs on the road and not on the cycle path. S-pedelecs are also not permitted on fast cycle paths or forest and field paths unless they are authorized for motor vehicles with an additional sign. The use of one-way streets against the direction of travel is also prohibited, even if they are cleared for bicycle traffic with an additional sign.

The Cologne police therefore advise riders to take part in a safety training course before their first ride to make it easier to get on or switch to an electric bike. During targeted
practical and theoretical exercises, participants are introduced to the special riding characteristics and also made aware of particularly dangerous situations.