You'll probably get a better answer on physics or electronics, but it's mostly a matter of voltage and damage not being that simple, especially when there are magnetic fields involved.
More voltage will drive more current through the same circuit. More current generates more heat. What happens from there depends quite a lot on exactly what the circuit is and the physics of any moving parts.
In the case of your drill and belt sander I would guess that what burned out was most likely the speed control. Speed controllers use semi-conductors to flip the power on and off with the cycles of the AC current. Semi-conductors (Silicon Controlled Rectifiers in this case) really don't like being subjected to voltages higher than they're rated for or excessive heat and tend to melt, explode, catch fire, or do other, violent things in response.
Your table saw and air compressor don't have speed controllers though. So if you subject them to a higher voltage, that drives more current, but nothing immediately faults and burns up. The more current results in more heat, but also creates stronger magnetic fields inside the motor. The stronger magnetic fields spin the motor faster. The motor spinning faster makes its fan push more cooling air. It's not actually that uncommon for motors to run cooler at higher voltages with the same load because the field effects are more efficient and the higher speed cools them off better. Couple that with most of the larger tools' electric motors being designed to run at either 110 or 220 because that makes them significantly more useful for an insignificantly higher cost and it's not terribly surprising that your heavy-duty tools could handle the higher voltage.
In fact, you might want to consult their owner's manual and/or the spec sheet of the motors they contain and see about just switching them over to 220v permanently. If they were designed to to that they'll run cooler and last longer plus they'll use the electricity more efficiently so it will cost you less to operate them, and you already have 220v available, you just need to put a proper socket on it.