Airspeeds play out a little differently when on the ground versus airborne, when the airplane becomes part of the overall fluid of the airstream. I think I’m reading you right when you say you want a breakdown, so here goes:
Indicated airspeed (IAS) is the dynamic pressure (Q) acting on the pitot tube. As you discovered, it’s unaffected by a change in wind (unless it’s a very sudden change) because the airplane is part of the whole flow, rather than affixed to a point and simply measuring what goes past like we do on the ground. A free balloon, for example, will move with the airflow, thus traveling over the ground, but have an indicated airspeed of zero (in steady winds). IAS is calibrated for standard temperature and sea level pressure, which will come into play later.
Calibrated Airspeed (CAS) is indicated airspeed corrected for instrument error and position error. You’ll see this especially in light aircraft at low speeds and maybe full flaps. CAS is technically the correct airspeed to make all further airspeed conversions and calculations, but at higher airspeeds it is usually close enough to IAS that we just use IAS. CAS conversions are particular to the aircraft and can be found in the aircraft POH.
True Airspeed (TAS) is CAS corrected for non-standard pressure and temperature. As you climb, let’s say you’re moving the same exact speed through the fluid of air, but since the air is less dense as you climb, there are fewer total molecules entering the pitot tube. So your actual speed through the fluid is your TAS, but the as the density of the fluid drops, your CAS drops with it. The result is that for a given CAS, the TAS will generally increase by about 2% per 1000 feet of altitude above sea level. This is why an airliner at 35,000’ might have an IAS (dynamic pressure) of 250kts, but is actually going maybe 450 knots through the air (TAS). At an extreme, a vehicle in orbit may be traveling thousands of miles per hour (TAS) but has an IAS of zero because there aren’t enough (or zero) molecules of air to register on a pitot tube. Warm air also affects the relationship between CAS and TAS, as it is less dense. So even at sea level, on a hot day your TAS will be higher than your CAS, and vice-versa for cold. This is one reason we chew up so much runway when taking off or landing on a hot and high altitude day.
Groundspeed (GS) is when you add (or subract) the total movement of the fluid of air to the TAS, dependent on how the velocity vectors interact. More simply, it’s the exact amount of speed relative to the ground.
There are also Mach numbers and equivalent airspeeds that deal with compressibility, which come into play when you get fairly fast, but I’m keeping this simple, in the GA realm.
The best aviation resource for all of this is the Pilots Handbook of Aeronautical Knowledge (PHAK). There are many others, but this one is official and free (well, courtesy of the US taxpayer).