unity3d - What is the exact difference between the game and game engine? -

i thought game engine unity or unreal. have editor scene editor, physics library, scripting editor , tools improve workflow of developer. furthermore, thought game engine should independent of game.(i.e.) game engine should not have game logic in it.

however, watched game engine video , totally confused. https://www.youtube.com/watch?v=gk7nta7a2vk . in game engine video, don't see game engine anywhere because seemed though professor developed game straightaway.

i hope can explain exact difference between game engine , actual game. know if worth developing game engine or better develop game straightaway, assuming going develop scratch in both cases.

game engine framework building game. has tools such map editor, animation editor, visual ai behavior editors etc. has scripting languages java script, c#. examples unreal engine , unity , cry engine.

but game in other hand final product created using tools inside game engine. using game engine game designers can make games without warring complex systems such rendering, ai , physics etc.