For a 2 kohm load, typical output voltage swing Op-Amp #1 is 13V, and the minimum is 10V with a 15V power supply. Its maximum supply voltage is 22V. Let's say I have another op-amp (Op-Amp #2) that has a typical output voltage swing for a 2 kohm load as well of 12V and a minimum output swing of 10V with a 15V power supply. Which op-amp do I use if I want an undistorted Vout peak voltage of 12.5V? Any help is appreciated thanks.
I suggest that you study some opamp datasheets, for example the one for the TL071.
Note how (in table 6.10) it says: Vcc = +/- 15 V and the output voltage swing with a 2 k ohm load is then +/- 10 V (minimum value). That means that the output can be driven
at least 5 V lower than +15 V (so +10 V)
5 V above the -15 V rail (so -10 V)
That "5 V distance from the supply" is important, compare that for both opamps and in combination with their maximum supply voltage rating you have an idea which one is more suitable.
Using the minimum value is important as that means a swing of +/- 10V or more swing which is always good.
A typical output swing of say +/- 12V means that on average this model opamp can output +/- 12V but you can expect that many samples ("monday morning opamps") cannot make it and only can do for example +/- 11 V. That you want to avoid if your product goes into mass-production. So focus on the minimum value.
Both amplifiers are guarranteed to produce 10 V into 2k with a 15 V rail. You want an undistorted 12.5 V. Neither amplifier is guarranteed to give it. If you're designing a product for sale, then neither amplifier will do for you.
However, any particular example may give you 12.5 V. If you're building a one-off for yourself, then get one and test it. The one with typically 13 V output is perhaps more likely to give you 12.5 V than the one with typically 12 V output. Try #1 first.
Amplifier #1 seems to have an advantage that it will accept 22 V, so you have the option to increase the rail voltage above 15 V, whereas #2 will not. Do beware though that 22 V might be its absolute max, which is not a recommended voltage to run it on routinely.