I have been told that the movement of electrons is like a chain on a bicycle, however on videos for batteries i see that there is a charge seperation and when a wire is connected, these electrons flow through the wire to the negative terminal. The chain analogy maybe refers to applying voltage when the no of electrons are constant?
The most important things to take from the chain analogy is that the elecrons in wires like to keep the same spacing, mostly confine themselves to flowing inside conductors, and don't themselves constitute particles of electric energy.
Actual electron behaviour is much more complex, quantuum physics and all that.
There are lots of useful analogies to visualize the electrons flow. The bicycle chain is a good one.
But my favourite one is the flow of water molecules in a river.
It has the following similarities to electron flow in a conductor:
1) A height difference is needed for water molecules to flow (vs. voltage).
2) Although water in a river flows very slowly (vs. electrons few cm/s) the throughput of water in a river can be huge (vs. many Amperes).
3) Steady flow, i.e. no matter how long the river is, there’s always almost the same amount of water molecules flowing in the river (vs. steady flow of electrons in conductor)
4) If the river is small, there’s less water molecules to flow through it (vs. resistance of the conductor)