What is the difference between the electrical components on a micro-chip and ones on an eyes-observable circuit?
Discrete transistors are packaged in various ways. Some of the earlier designs were packaged in metal cans about the same size as the small black-plastic packages you probably see on a motherboard.

Here's a phot I took just now, the ruler is marked in mm (the "1" is 1 cm).


Photo by RedGrittyBrick

Here's an enlarged photo of one opened up, 


Image by Rolf Süssbrich Rsuessrb

You can see that the actual transistor is much much smaller than the metal container.

As other people have pointed out, you can make the transistors much smaller still - so long as they don't need to carry much electrical current.

Here's a picture of a transistor of the sort of size you'd find in a CPU


Image from TomsHardware