Represented in this diagram. I want the particles which currently emit from all points to shift towards a vector represented in gray then move down based obviously on a negative vector. The question is, how do I get the particles to shift as represented by the red arrow ?

You can use two different forces. Stagger their activation to form a series of actions.
In this example [www.sidefx.com] you can see two forces at work. One, the volume, causes things to rise. The other is simply a force that moves in the X axis.

This is the same technique as having the particles flow along the surface ?

No, surfaces are just collision objects in this setup. But if you carefully control wind you can blow particles along a surface.

Not sure if I understand it right but you can drive the particles by creating a vector field with the surface, then drive the particles with sopvectorfield and fieldforce in dop.

@benc - What do you mean creating a vector field with the surface ?

You can set velocity attribute to the surface and convert it to a vector field with fluid source.