What's the difference between these two lamps? They're the same length and diameter, so I'd think they'd be pretty much interchangeable. Is the cathode heating voltage different or something?

The F17T8 is a 265mA lamp just like the F32T8, and many F32T8 ballasts are rated for F17T8. The F18T8 is designed for use on preheat F20T12 ballasts. I read on this site that some members have tried interchanging the F17 and F18 tubes with no problems, while others have had unreliable starting. I believe you are correct that the cathode voltage is different as well.

F18T8 are the european 18W T8 retrofit lamps for 20W T12 (F20T12). They can't be operated on rapidstart or trigger-start, because their starting voltage is higher than of 20W T12.
For this reason, they can't rectify at EOL on series preheat choke at 220-240V, and will just flash until the starter will get stuck.

I use sylvania crocktrons f17t8 on preheat 120v and have no problems.

The F18T8 would work practically only on F20T12 preheat. As Dor mentioned, they require way higher voltage for the ignition, so the F20 RS ballasts won't start them.

The sylvania quacktronic rapid start ballasts are fine with these.

I meant a "classic" mains frequency ballasts.

The quicktronic are rather a programmed start ballasts - first applies just the electrode heating (there could be voltage present across the lamp, but not sufficient to strike it) and only after some time boost the voltage to ignite the lamp.

The slow frequency sweep used with many ballast designs may give the impression the lamp brighten slowly (similar to the RS), but the reason for that brightness change is completely different (in RS it is caused by the electrodes slowly gaining emission, with the resonant frequency sweep ballasts it is the ballast circuit, what increases the delivered power gradually)

Or when the PTC (used in some Quicktronics) is still hot, the start is rather instant start with assisted electrode heating - it isn't a RS, as the discharge is ignited instantly, but it electrically aids the heating of the electrodes until they reach the emission temperature.
Here it may gradually gain the brightness as well, the reason is, at the cold electrode mode the ballast is not able to deliver full current (it would mean way higher than rated power), so as the electrodes reach emission, the voltage drop lowers, the current, so brightness increases. From the RS ballast the difference is, the discharge is already present even when the electrodes are still completely cold.
Normally this stage is not visible, because the dimmer cold electrode mode lasts only 100ms, the filament are fed by really huge currents (many times their normal rating; it does not overheats them, because once they reach the emission temperature, the heating current stops)...

I have had NO problems with the F17T8 or the F18T8 starting on trigger start....

Is it using the older style rapid start magnetic ballasts? Those can crank out a fair OCV so it may work.

But then such ballast will suffer (or better said the lamps on it) from premature cold starts (when the lamp ignites before the electrodes are warmed up), leading to faster wear...

It is not that big problem top make a RS-like ballast (with filament heating) to start the lamps, but it is nearly impossible to make it so, it will reliably start the lamps only after they warm up, without igniting them earlier.