For starters, “electric engine” is not in common use. Instead, the phrase “electric motor” is used. Technically, “engine” and “motor” are interchangeable terms, but the common convention of using motor for electric helps distinguish the two.
OK, on to the physical differences. For starters, an electric motor typically consists of just 2 parts; the stationary stator and the rotating rotor. In contrast, a gasoline engine consists of hundreds of moving parts. Most modern EV motors are of either the AC induction or permanent magnet switched reluctance type.
Being much smaller than a gasoline engine, electric motors are typically located between the wheels being driven. A simple gearbox and half-shafts directly connect the motor rotor to the wheels.
For rear wheel drive EVs, the motor is in the back. Most all-wheel drive vehicles have a motor at each “axle”, while a few (e.g., some Rivian models) have a motor on each wheel (two per axle).