A Vector 3 is a set of 3 numbers. X,Y,Z Example: (1, 3, 5)
A Transform is a game objects position, rotation, and scale in the scene, and can be seen in the inspector when you have the object selected.
A GameObject is anything that is in the scene. Game Objects have Transforms if they are in the scene, because they have a position, rotation, and scale.
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Transform is a property attached to GameObjects. For example: Your scene is a 3D-Room. Your GameObject would be then a Point in that room with a Position, Rotation and Scale. These 3 variables are Vector3’s.
And finally a GameObject is your Object in your Hierarchy. It can be a 3D-Model, soundfile or even an empty object with components (scripts and stuff) on it.
(Excample) If you want to disable a GameObject you have to do this:
gameObject.SetActive(bool);
You also can call GameObject from Transform and Transform from GameObject:
transform.gameObject;
gameObject.transform;
Connection between these 3:
GameObject contains Transform,
Transform contains Vector3 (position).