First, is my description of DC is correct ? Because if my understanding is wrong, there is no point to move further.
Technically they are both AC circuits, there is no steady state current, which would make them AC. DC is 0Hz, AC is everything else (or more associated with sine waves, but doesn't have to be).
If some load is connected then there would be constant charging / discharging currents AND, along with it, "main" current. I.e. constant surface charges redistribution due charging currents would create constantly increasing, decreasing and flipping electric field inside wires and resistor. Again, as result, we got "main" current due this inner electric field. But since the field is constantly changing now, electrons just slosh back and forth.
Anyway, is this wrong or acceptable description ?
This is where your getting confused: The carrier in an AC circuit is not the electron it is the electric field on the inside (surface currents) and outside of the wire. This is where the bulk of the energy is being transferred, the wire acts like a wave guide. If you integrate all the energy being carried by electrons vs the electric field on the outside of the cable, very little of that is transferred by the electrons themselves. Electrons are not needed to carry electromagnetic energy, or radios would not work, the carrier is the photon.
The reason for this is the inductance of the wire itself, with higher frequencies they prefer lower impedance of the outside of the wire. This is called skin effect
Source: https://www.allaboutcircuits.com/textbook/alternating-current/chpt-3/more-on-the-skin-effect/