Ah - yes, when you're on a decent device, that would be great, thanks
Having been to look things up I think I was getting confused between some aspects of vacuum and air - I was thinking that air brakes, like vacuum brakes, "charged" both sides of the cylinder and then "discharged" one side of it to apply the brakes. On checking I find that they have a separate local reservoir which is connected via the magic valve to an uncharged brake cylinder to apply the brakes, and the cylinder is vented locally to atmosphere to release them. Is that more like? It makes sense in terms of what you say about applying vs. releasing. But I am still thinking that vacuum brakes rely on discharging the vacuum in the brake cylinders via the train pipe and the driver's brake valve, which seems to be at odds with what you're saying, so it would be handy to have the pukka explanation, thanks.
Vacuum brakes work, as the name suggests, by the locomotive's exhauster removing the air from the train's braking system to a pressure of between 21 and 25 inches of mercury below atmosphere (hereonin referred to as inHg) depending on the design of locomotive (ex GWR ones typically use 25 whereas anything else uses 21).
In each brake cylinder there are two sides, one (the reservoir) which is protected by a valve so that air can be removed but not re-enter, and the other which is maintained at the same pressure as the train pipe.
When both sides of the cylinder are at equal pressure (whether that be atmosphere, 25 inHg, or anywhere in between) then the brakes will be released.
We'll assume now that the locomotive has created a 21 inHg vacuum in the system.
To request a brake application, the driver (or Guard, or passenger via a Passcom cord) will open their valve which allows air into the system, which increases the pressure in the train pipe, let's say, to 13 inHg.
The train pipe is connected to a device on each cylinder called a DA (Direct Admission) Valve, which detects the increase in pressure and admits a proportional amount of air from outside - not the train pipe - to the brake cylinder.
Owing to the non-return valve we talked about earlier, the reservoir side of the cylinder remains at the same pressure (21 inHg), but the other side is higher (13 inHg), and it is this pressure differential which moves the brake apparatus to physically apply the brakes.
Releasing the brakes, the locomotive simply runs it's exhauster which removes the air from the train pipe and brake cylinders to return them all to a pressure of 21 inHg, thus there is no pressure differential and the brakes release.
You've pretty much nailed it now with regards to air brakes. The train pipe is charged to a high pressure and to apply the brake the pressure is reduced.
Each vehicle has an auxilary reservoir (charged from the main reservoir pipe where provided or via the train pipe where not), and subsequently a device called a distributor or triple valve (although I like the term "Magic Valve" so I'm going to steal that from now on

) in a similar way to the vacuum DA valve detects a drop in the train pipe pressure and then admits a proportional amount of air from the auxiliary reservoir into the brake cylinder; again there is a pressure differential acting in the brake cylinder which moves the apparatus to apply the brakes.
When the 'Magic Valve' detects the train pipe pressure is back to normal then the air is released from the cylinder returning both sides to atmosphere and thus releasing the brake.