I don't understand why it's so complicated.
The engine is a diesel engine. Just like a tractor, it makes noise and smoke and is also called an engine (brands include: Cummins, Carter, Deutz, Rolls-Royce, etc.)
A generator is an electric current. The output will not make any noise (brands include: Faraday, Stanford, Leyson, Ma, Inge, etc.)
The motor and generator are connected with screws to form a generator set (the production companies include: Jin Dongkeli Generator·Xiecheng Generator Kangda Yecheng Xilipu, etc.)