What actually flows, current electricity or charge?

 This is my answer to SE EE question What actually flows, current electricity or charge?

My answer

To intuitively understand circuits, it is enough to realize that something like a pump (source) produces something like pressure (voltage) that causes something like fluid (electric current) to flow from where it is a lot (the positive source terminal) to where it is a little (the negative terminal) encountering obstacles (resistance) on its way.

Then we need to realize what the connection between these pressure-like, flow-like and impediment-like quantities is (Ohm's law) and to see where currents flow (topology).

Finally, it remains to be seen (in a most general way) what the basic circuit idea is.