I'd refer to it as "instantaneous standby capacity", like the bypass capacitors on my circuit boards.
Yes, in an abstract sense you're right, but of course bypass capacitors store picojoules or nanojoules of energy, whereas spinning reserve has to be able to supply hundreds of kW in one or two revolutions of the alternator shaft; also bypass caps are acting to (try to) hold a DC bus at a constant voltage, whereas utility spinning reserve is trying to hold an AC bus at a constant frequency.
There are disturbances on the order of microseconds (lightning strikes and squirrels shorting out phases) of course, but those are taken care of by other means.
On the power grid's "infinite bus," an alternator that falls behind due to RPM drop becomes a motor, sucking energy from the grid. Thus the problem becomes one of phase control, really. Each alternator is a synchronous device that must be phase locked to within a very small amount (like a fraction of an electrical degree) of the grid at large.
If there's a sudden load change, at least two things happen fast: one is that the exciter current of the alternator is bumped up to supply enough field to keep the alternator's output voltage high enough so that it is a net source to the grid. The other is that (as I said before) more energy is supplied to the prime mover to keep the drive shaft in phase with the other devices on the grid. That happens a little more slowly because the amount of mechanical energy stored in the spinning turbine-alternator rotor assembly is hundreds of millions of joules, and inertia will carry the device for a few revolutions.
I forgot to complete my thought before. The problem with wind power is that — well — it varies with the breeze. Since the utility's customer's demands do not vary with the breeze, the utility has to supply spinning reserves to back up any wind turbines that are on the grid; the amount (I was told) they plan for is 75%, meaning each kW of wind turbine has to have 0.75 kW of spinning reserve somewhere, ready to take over if the wind dies off.
This of course costs the utility money, and that amount of money subtracts from the economic efficiency of wind turbines. The same is true of photovoltaics; if a cloud obscures the sun, and your PV installation suddenly drops from supplying 50 MW to 5MW, that's like someone just fired off an electric arc furnace on your grid with zero warning.