What is the difference between Integrated Circuits and Printed Circuit Boards?

to the man in the street: An integrated circuit is something like an eprom ( a small unit like a chunk of chocolate) that is usually soldered onto a circuit board.
A printed circuit board is a slab of board with holes in it. (like a smaller version of a pegboard) that has lines of copper or similar printed on it for the purpose of connecting all the integrated circuits and resisters together.

short answer = Size

breadboard =
insulation with holes where you mount components
and run wires to interconnect them

printed circuit board=
insulator with copper laminated. copper is etched away to leave wires .. sometimes in several lamentations components are soldered into holes drilled in the wires

Hybrid module=
usually a ceramic insulator with copper laminated wires
components in beam lead packages electron beam welded to the copper

integrated circuit =
the insulator is the substrate usually a diode done over most of the Si wafer in the first diffusion components are built by diffusing different materials in more and more layers
packages or carriers
7400 ic dip 1" x 1/2" surface mount 1/4" x 1/8" beam lead .050" x .025"

SSI MSI LSI small scale, medium scale, large scale... integration
has to do with the color of the light red light 760nm won let you work much smaller than 1 micron... blue light 350Nm maybe 0.5 micron uv perhaps .2micron
xrays gamma rays are a bit more difficult to mask and control
so electron beams are used for smaller stuff perhaps tunneling electrons can bring it down some.
perhaps an order of magnitude breakthrough will give us nanotek