There are four distinct spaces that objects get transformed into:
An object starts in Model Space (generally), then get's multiplied by the world matrix, putting it into World Space.
Then that matrix gets multiplied by a view matrix putting it into view space.
Then that matrix gets multiplied by the projection matrix putting it into Projective or Homogenous space.
Homogenous space is where all on screen vertices are in a Unit Cube. This is where the "w" divide happens, clipping the 3D locations into a 2D screen space coordinate system.
There is also another, less used, transform applied here, called the viewport transformation. It's what determines the bounds of the 2D locations.
You can read more about the spaces here: