Too long for a comment to Alexander's post, so I post it as my own comment:
CAS is IAS corrected for installation anomalies, mostly around the pitot tube. The correction itself is very minor, so most people just ignore it. Some airplane handbooks have CAS / IAS correction tables in them. At larger speeds (jet planes) CAS vs. IAS becomes more important, but you are still a beginner and therefore won't be flying the Gulfstreams soon.
IAS/CAS measures what "grip" the plane / its wings have in the air. Therefore, for the same speed of a motion object in space, it is lower for thinner air and higher for denser air. It's why you look at IAS for maneuvers and take-off and landing, because you need to know how the plane "feels" the air.
"TAS is used primarily for navigation" Not true. What would TAS have to do with navigation? Why? TAS corrects for non-standard pressure and non-standard temperature if properly done on an E6B.
"if your aircraft generates the same lift, you IAS will be the same". Assuming same pressure, temp, and humidity (very minor factor), that is correct.
Your moon example ... there is no airflow or lift on the moon. Which is why propeller flight has a certain maximum height. I forgot what it was, someone fill my blank here, but it is something like 30 thousand feet or 40 thousand feet. You aren't allowed to fly higher with props, because the props would have no "grip" in the air. It's why space rockets are "jet engines" and not proppies.
"TAS on the other hand has nothing to do with the aircraft performance, it just shows how fast your are moving in a body of air" which has a lot to do with performance :)
"I don't even know if TAS is needed in flight if you use GPS with ground speed. Guys, who know what else is TAS for in flight if you have GPS, please share." TAS was used for decades, long before GPS was around. Oftentimes for a specific flight you want to look at the current ground speed, because that tells you how fast you are going over the specific terrain, therefore is the end result after winds. So GPS is useful here, it is the "end result" after IAS, CAS, TAS, pressure corrections, temp corrections, wind corrections. Just measure the end result instead of computing it with assumptions. But oftentimes you want to know TAS and do not want to include winds. For example to compute some performance data for your plane. You might be interested in figures like distance per gallon, to make performance figures comparable to well-known car figures. So you use a timer, look at the fuel flow (this exercise can be done rich-of-peak or lean-of-peak or ideally both) and compute distance per gallon, or gallons per mile. Here using the GPS to have "auto-wind correction" would be wrong, because the wind would significantly distort the computation. So you use TAS, that is independent of wind direction. Doing this exercise with strong tailwinds or strong headwinds would give the same results, because your TAS isn't impacted by winds. But that means TAS is very useful for performance calculations, contrary to your claim (see previous para).
Your next para shows a misunderstanding of CAS. With CAS we want to correct IAS for installation error of the pitot tube.
Rule of thumb for TAS: add 2% to IAS for every thousand feet of altitude. For example, at 10 thousand feet your IAS (proxy for CAS) is 120 knots, you would add 20% of IAS and get 120 + 24 =144 knots TAS. This ignores temperature error, which is much less of a factor than pressure. It is actually 1.6 % for every ten thousand feet, but people round it to 2% to make the math a tad simpler. But be aware: this rule of thumb ignores temperature error!
Regarding the yellow arc question from Sergey: From the book: "Yellow arc—caution range. Fly within this range only in smooth air and then only with caution" It is still a speed that has to do with the airflow over the plane, therefore IAS is used, not TAS. We don't fly in the yellow are when we are in gusts, because a gust can significantly affect the wing loading. Thus we don't care about how fast we fly through space, but how fast we fly through the surrounding air. It's IAS that tells us how the plane "feels" the air surrounding it.
I recommend you read some the FAA's manuals, the AFH and PHAK are excellent resources that explain all that. From your questions I glean you have more "ground school" ahead of you. The FAA's manuals are here: https://www.faa.gov/regulations_policies/handbooks_manuals