When I helped an interlocutor learn about metabolism, we made an analogy between steam engines and cellular respiration. I find that people (at first) know steam engines better than cellular respiration, so I show the analogy here as a guide to cells assuming you understand engines. You could also use it in the other direction, if you learned about cells first.
If you go far enough into the details, the analogy will break down, as would any analogy. But this one holds more precisely than I or my interlocutor expected.
Glucose in the cell is like coal in the boiler. The boiler burns coal; likewise, the cell runs glucose thru the citric acid cycle (after glycolysis). The fire (the citric acid cycle and electron transport chain) heats the water (adenosine diphosphate, ADP) to a closely related, higher-energy form (adenosine triphosphate, ATP), which is steam. The steam (ATP) pushes a turbine (enables cellular work), condensing back into water (ADP).
With some changes to the engine, you can use oil in place of coal. Likewise, with some changes to what the cell does (beta-oxidation in place of glycolysis), it can use fat (or ketone bodies) in place of glucose. The fire of the boiler is essentially the same, and once the cell gets acetyl-CoA from carbs or fats, it uses the same citric acid cycle and ETC in either case.
Most of the boiler corresponds to the mitochondrion. The pipes carrying water to be boiled are like ATP synthase. ATP synthase is an enzyme embedded in mitochondrial membranes, which lets protons across the membrane in a way that phosphorylates ADP to ATP.
In some animals (including humans), the mitochondria in brown adipose tissue let pumped protons cross back for heat rather than ATP. This is like exposing the building around the steam engine to the heat of the boiler.
>heats the water (adenosine diphosphate, ADP) to a closely related, higher-energy form (adenosine triphosphate, ATP), which is steam.
I would say protons are the steam, not the ATP/ADP. The electron transport chain “pressurizes” protons by pumping them, and then the protons flow through the ATP synthase “turbine”.