Flight
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Altitude and the dot field around the nose are exaggerated so you can see them change; the four numbers themselves come straight from your inputs.
Wind is simplified to a straight head/tailwind component here (positive = headwind, negative = tailwind). For the full wind triangle with a crosswind, see the E6B trainer.
The chain
Which speed matters?
Four speeds, one flight
The TAS correction here uses the same rule of thumb as the E6B trainer (roughly 2% per 1,000 ft of pressure altitude, plus 1% per 10°C warmer than standard), close enough for training and flight planning, not a certified performance figure. Compressibility correction (CAS to EAS) is skipped entirely, it's under 1 kt for typical trainer speeds and only starts to matter above roughly 200 kt or high altitude.
IAS, what the gauge actually shows
The airspeed indicator is a differential pressure gauge: it compares ram air pressure from the pitot tube against static pressure from the static port, and the needle moves with the difference. Indicated Airspeed is that reading straight off the dial, nothing has been corrected for yet.
See the Pitot-Static Lab tool to explore what happens to this reading when part of that system is blocked.
CAS, correcting the instrument itself
No installation is perfect: the airflow around the pitot tube and static port is slightly disturbed by the airframe itself, and that disturbance changes with angle of attack, so it's worse at low speed and high flap settings. Calibrated Airspeed is IAS with that instrument and position error removed. It's usually only a few knots, but the aircraft's official V-speeds (Vs0, Vs1, Vfe, Vne...) are all defined in CAS.
TAS, correcting for thin air
CAS is really a measure of dynamic pressure, and dynamic pressure depends on both how fast you're moving and how dense the air is. Climb into thinner air and the same dynamic pressure, the same CAS, now needs a higher true speed to produce it. True Airspeed is that actual speed through the air mass: it grows with altitude, and with temperatures warmer than the ISA standard for that altitude.
This is why TAS is what performance charts, range and fuel planning for a cross-country actually want, not IAS.
GS, correcting for wind
TAS describes your speed relative to the air mass, but that air mass is itself moving relative to the ground. Add the wind (a headwind subtracts, a tailwind adds, and any crosswind component needs a full wind triangle) and you get Ground Speed, your actual speed over the ground. This is what your ETA is really built on, not TAS.
For the full wind triangle with a crosswind component and wind correction angle, see the E6B trainer.
Why the difference actually matters
Each speed answers a different question. Is the aircraft close to stalling right now, read the airspeed indicator, it's built to answer that (IAS/CAS). Planning fuel and range for a long flight at altitude, use TAS from your performance charts. Working out an ETA or how much fuel you'll actually burn to a waypoint, that's GS. Mixing them up, for example using TAS where the checklist wants IAS, is a real and avoidable source of error.