Physics engine comparing game engine

Do not mistake a physics engine for a game engine. A physics engine only simulates a physical world without anything else. There are no graphics, no logics, only physics simulation. On the contrary, a game engine, most of the time includes a physics engine paired with a render technology (such as OpenGL or DirectX). Some predefined logics depend on the goal of the engine (RPG, FPS, and so on) and sometimes artificial intelligence. So as you can see, a game engine is more complete than a physics engine. The two mostly known engines are Unity and Unreal engine, which are both very complete. Moreover, they are free for non-commercial usage.

So why don't we directly use a game engine? This is a good question. Sometimes, it's better to use something that is already made, instead of reinventing it. However, do we really need all the functionalities of a game engine for this project? More importantly, what do we need it for? Let's see the following...