There are five basic types of airspeed: indicated (IAS), calibrated (CAS), true (TAS), ground speed (GS), and mach.
The most basic, airspeed given is the indicated airspeed. IAS essentially gives the speed that air is traveling over the wings to generate lift. IAS is generally not a very accurate indication of how fast the aircraft is actually traveling, but it does indicate whether or not the aircraft is flying. All things remaining constant, an aircraft will always stall at the same IAS given a constant configuration (CLmax AoA) at all altitudes.
Calibrated airspeed is IAS corrected for known instrument deviations. Usually CAS is very close to the actual IAS and varies by just a few knots.
True airspeed is the actual speed of an aircraft through a column of air. True airspeed is CAS corrected for density altitude (ie, corrected for air density, temperature, humidity, etc...)
Ground speed is simply the aircraft's speed over the ground, and it is derived by taking TAS +/- a tailwind or headwind, respectively. GS is used, among other things, to determine the time it will take to travel a certain distance. The GS of an aircraft is very comparable to the speedometer in a car, they both indicate speed over the ground.
And last, the mach number indicates how fast an aircraft is traveling through a column of air in reference to the local speed of sound (LSOS)--the formula is TAS/LSOS. It is important to note that the LSOS changes drastically with temperature, so LSOS is typically faster at lower altitudes and slower at higher altitudes (barring a non-standard condition like a temperature inversion). Mach has absolutely nothing to do with ground speed, so even though you might have a tailwind pushing your aircraft making the ground speed faster than the speed of sound, your mach number may indicate well below mach 1 because, remember, mach is only relevant to the speed of the aircraft through a column of air in reference to LSOS.
PS, Skipper, haha, I have never met a single pilot that actually still uses a slide rule anymore. And that's a good thing because I'd probably crash the plane trying to read that aggravatingly small print.
@Skipper, the T-34 is a good aircraft, they are just recently retiring the T-34 fleet from the Navy and replacing them with the T-6. I also think its funny that you reference Sportys, some guys live and die by that website :)