I'm not sure I understand your question, but I would say that they are both the same thing.
We use 4x4 matrices to represent transformations, and due to the associative property of matrix multiplication, you can represent multiple affine transformations in a single matrix, and then apply that transformation to as many points as you want.
3x4 matrices are a ...
The names "world matrix" and "model matrix" are just terminology, and are not 100% standardised, so depending which source you read you may see them being used to refer to a number of different things.
Generally speaking, your 3D scene will consist of the following:
Objects that move around in the scene.
Static parts of the scene that ...