There are lots of different airspeeds out there, which work like this:
Indicated Airspeed - What you can see on the dial
Calibrated Airspeed - this is what you would see on the dial, if the system were perfect. It may have been nearly perfect before you wrapped an aeroplane around it, but because you did, and because there are small mechanical and pressure distribution errors within the system, CAS is not the same as IAS. The difference between CAS and IAS is PEC - Pressure Error Corrections, which are what are shown in the chart in the operators manual.
Most of the errors in the system will be in static pressure, rather than pitot pressure. So, this affects altitude as well, which explains the other graph in the manual. It's normal for the aviation boffins who create the graph to assume that all errors are static errors and work it out that way.
Equivalent Airspeed - this is CAS, modified for the fact that the ASI are designed on the assumption that air is incompressible. Below 10,000ft and 0.6 Mach, you can assume that air really is incompressible so EAS = CAS. Otherwise you can correct using a chart, or a whizz-wheel.
EAS is the most important number for structural engineers - it is basically a measure of how many air molecules pass the wing per second, and so defines all the structural loads.
True Airspeed - this is EAS, modified for changes in density. and is how fast you're actually going through the lump of space you (and a load of air) occupy. TAS = EAS divided by the square root of relative air density.
Groundspeed - this is TAS, corrected for wind. Also however, it's what you can read on a GPS, so most instrument calibration nowadays starts with GPS speeds and works backwards.
Temperature corrections to altitude are nothing to do with PEC, and are everything to do with different relationships between temperature, pressure and altitude. Your altimeter is calibrated for ISA, and will read an altitude based upon ISA conditions; if temperatures are below ISA, then the air is more dense for a given pressure, which leads the altimeter to overread - so if you were trying to clear a mountain on a below-ISA day by reference to the altimeter (a pressure instrument) you can clip the top. The standard corrections are there to avoid this. This is called Temperature Error Correction (TEC) not Pressure Error Correction (PEC).
The standard number usually taught is 4ft per 1000ft per °C. So let's say you're flying at 8,000ft on an ISA-10 day: 4 ft x 8 x 10 = 320ft, so you'll be 320ft lower than it says on your altimeter. If the mountain is 7,800ft high, you need to climb! If the mountain is 6,800ft and you're flying IFR, then you still need to climb because you're failing to maintain the legal 1,000ft separation from terrain below.
G