What are the differences between the circuits you find in your house and the circuits on a microchip in a computer?

In a physics sense, none. But in an electrical sense, A LOT.

Microchips operate on DC (Direct Current) electricity, typicaly at 12, 5, 3.3, and 1.0-1.5v rails.

Computer microchips also may contain hundreds or more of individual circuits, whereas the average house only has a limited number.