You've already sorted this out, but the lesson here is simple: Don't ever assume anything.
Determining 220 vs 110 at the panel is fairly simple. You have a phase A and B in your house, which come from each side of the transformer. The transformer is center-tapped to ground, and this is your neutral wire.
"Voltage" is really just a measurement of potential difference between two points, and so if you think of it that way, the voltage between A and B is 220V, and the difference between A and neutral or B and neutral is 110V.
In your breaker panel, every other row of breakers is a different phase.
To get 110V power, you need a neutral wire, and a hot wire from either phase A or B (it doesn't matter which). So any single breaker, like #3, is only supplying 110V power.
To get 220V, you need one hot on phase A, and one on phase B, like the 220V breaker at the bottom right (#4/#5).
This picture also includes some tandem breakers (the one currently being installed is a tandem), in which case both circuits are on the same phase. That is, both #1 and #2 are on phase A. If you measure the voltage (potential difference) between #1 and #2, you'll get 0V.
Voltage between #1 and #4 is 0V, and between #3 and #5 is also 0V.
Voltage between #3 and #4 is 220V, since they're on different phases.
Note though, it's against code to use single circuit breakers to run a 220V circuit, since if the power trips, you want all the power to trip, not just one side (since that would leave 110V hot).
The other huge tip-off at the circuit is the wire colors (though again, never assume, always test). There aren't a ton of requirements for wire colors, other than two: white means neutral, green (or bare) means ground. If you use a white wire for something other than neutral (common in a light switch, for example), it must be indicated on both sides, usually by wrapping a piece of red or black tape around it. Black is hot.
The next most common color is red, which has two very typical meanings:
* switched, which you'll commonly see in duplex receptacles where one is constant, and one is controlled by a switch
* hot for 220V, which is the case here, where red is the opposite phase from black, to provide 220V.
To sum up:
- In the panel, a double-sized breaker on the circuit means 220V
- At the branch, not having a white neutral wire means you can't get 110V.
Best Answer
Switching GFCIs line-side tends to make them a bit cross
Plug-type GFCI devices revert to the "tripped" state when unpowered, unlike receptacle-type designs, which mechanically latch in both "tripped" and "untripped" states. This was done to allow them to protect against an open neutral, which'd otherwise defeat the GFCI protection and make it impossible for it to trip.
However, this makes them incompatible with being switched on the line side, as you see here. The solution is to move the GFCI protection to a location upstream of the timer -- GFCI breakers are ideal here, but a receptacle or deadfront GFCI can be used upstream of wherever the switch or timer is. Once you've done this, you'll have to remove the GFCI plug from the end of the plug-in pool's cord and replace it with a regular plug, with a big note on it saying "FOR USE IN GFCI PROTECTED OUTLETS ONLY".
Either that, or you can remove the plug and wire it into a timer that's then wired in series with another length of appropriate cordage that is terminated in the existing GFCI plug, effectively moving the existing GFCI upstream of the timer...