How can ballasts tell what wattage a fluorescent tube is as in an F40 or F30

I don't think ballasts "sense" at all, except maybe higher end electronic ballasts. At least with magnetic types, they are set up for a specific current range and the lamp has to fall into that range of parameters to work properly.
I just recently noticed that single-lamp 30w and 40w ballasts are the same! I noticed that a single 40w fixture in a Lowe's display had higher surface brightness than the single 30w fixture, so this makes sense. If you look at the ballast label, you will see the wattage and current ratings the ballast can provide. Same with the 2-lamp 40w ballasts - most also run a 34w and 25w T12 lamp nowadays as well. But, if the ballast is set up for only 40w, 25 lamps will have a short life, and 34w lamps may damage the ballast. One of my ceiling fixtures uses a 40-34-25 2x4' T12 residential ballast that apparently puts out no more than 25w per tube. Even with 40w lamps in it, it's dim! But the lamps are lasting forever!
The simple chokes used with 15-18-20w lamps also seem to drive the lamp about 18w, so a 20wT12 lamp will be somewhat dimmer than it could be and a 15w lamp will burn a bit brighter.

I've often wondered about this myself.  I've wondered how 34 watt "miser" lamps can work on 40 watt ballasts.
I'm no expert on this, but as far as the range of sizes go, I would think the larger lamps (F40T12) would have a different voltage drop across them than the smaller ones (F30T12), and that may affect how the ballast runs them.

I think the shorter bulbs drop less voltage, so in turn the power dissipated is lower.

Yeah the 34w lamps are designed to have less voltage drop than 40w. In fact, the voltage drop is part of wattage calculation...volts times amps. For the magnetic ballasts, there are two main kinds that can act opposite on given lamps.

The NPF or normal power factor do not use a cap and when the lamp voltage increases...as in larger lamp, the current decreases, driving the lamp at lower power. For example, a 30/40w ballast will drive a 30w lamp at perhaps 30w but when connected to a 40w, the higher voltage drop lowers the current significantly and overall, a 40w lamp might be operating at 25-30w; hence, the 25w lamps that are designed for these "residential" ballasts.

A HPF or high power factor ballast uses internal cap and when lamp voltage increases, ie, larger lamp, current remains fairly constant, therefore wattage goes up. For example, a 40w HPF ballast might drive a 40w lamp at 40w but when connected to a 30w lamp, the voltage drops but the current rises very slightly so overall the wattage reduces with the lamp size.

Bottom line, A NPF ballast is most likely to overheat with too small of lamps while HPF would most likely overheat with too large of lamps...but if lamps were way too small on HPF, the current could still rise to dangerous levels too.

This is somewhat related to what is being discussed here, so I am going to ask this question:  Can an F17T8 lamp be run on a 14-15-20w standard choke ballast?  I would assume it would be ok, since the wattage is only 2 watts higher than an F15T8, and three watts lower than an F20T12.  I have wondered if an F17T8 would actually be brighter than an F20T12 when run on a 14-15-20watt ballast, since the tube is narrower and a choke tends to underdrive an F20T12 at around 18 watts.  I wonder if it would be more ideal to use a 17w T8 in my preheat fixtures?

Electrically, the F17T8 should be fine on that ballast. I ran one before and it worked good...though I didn't do any measurements. The only thing I noticed was that the lamp was a little stubborn at starting at first and not sure why.