The "cleaner" and the "primer" are EXACTLY the same,
The cleaner and the primer are not exactly the same, chemically or in function.
The MSDS for Oatey's cleaner lists the ingredients as
60-100% MEK (methyl ethyl ketone), 15-40% acetone
MSDS for primer lists the ingredients as
60%-100 acetone, 0-20% MEK, 0-20% tetrahydrofuran, 3-10% cyclohexane
The cleaner is used to clean up grimy pipe. It could be used solo before the installation of a compression fitting, or as an optional initial step before priming. I would use it for the latter before priming a pipe covered in grease, paint, or other similar grime, but it would be superfluous on new pipe. The general purpose of this extra step is to ensure the primer is able to properly soften the pipe's surface to accept the cement. If the primer brush is just wiping off paint, there is some likelihood that the pipe will not get primed properly and the joint could fail.
Cleaner aside, the primer is
not optional, even on new pipe. Its role is to soften the outer layer of pipe so the cement can solvent-weld the joint, instead of merely gluing it together.
Cementing PVC without priming it first is not much different from gluing it together with cyanoacrylate (superglue). You could do the same with copper and have a joint you couldn't pull apart by hand, but without fusing the materials the joint won't last under years of thermal expansion/contraction, pressure, vibration, etc. Hence the volume of stories earlier in this thread from plumbers repairing earlier unprimed work.
If it's worth doing, it's worth doing right.
EDIT: Cleaner is also useful for ABS. As someone noted earlier in this thread, you do
not prime ABS joints because the plastic layer around the pipe's core is thin. You can, however, use cleaner to prep them for ABS cement.