dual core and quad core is like the expansion from what hyper threading tried to do.
Dual core is literally 2 cores inside the CPU so it is essentially 2 CPU's in one, which means you can do 2 heavy CPU tasks at once. and it is very quick.
Quad core is the newest version of the multi-core revolution, quad core is a little expensive but is 4 cores in one, so, it is again double the speed of the dual core, as it acts as 4 CPU's being able to dealw ith 4 heavy CPU tasks at once with ease, or quickly get through 1 task as a team.
that is the difference between a normal standard core, a dual core, and a quad core.