For AC power wiring, you just follow your electrical codes.
Here's my cheat sheet for NEC.

This is just the standard NEC table with the "no go zones" grayed out.
Note that the green zone (aluminum NM and UF) is found in old work, and apparently is starting to be sold again, go figure. Someone makes a Copper Clad Aluminum NM cable. Wish they would offer it in SER instead, so we could use the higher amp rating.
If your wire and all your terminals are rated for 75C thermal rating, you can use the 75C column (barring 240.4(D)), otherwise you use the 60C column.
Ampacity doesn't care about voltage
Heat rise (which is what all this is about) is caused by voltage drop. Let's consider a 12 volt installation running 10 amps. The wire is quite long and has 0.1 ohm resistance. Ohm's law says voltage drop will be
Vdrop = I (current) x R (resistance)
Vdrop = 10 amps x 0.1 ohms
Vdrop = 1 volt
How much heat is that in watts?
P = V (volts) x I (current)
P = 1 volt x 10 amps
P = 10 watts
So at our 12 volt system at 10 amps, we have 1 volt of voltage drop (8%) and 10 watts of wire heating.
So let's look at the situation at 120V. 10 amps, 0.1 ohm wire.
Vdrop = 10 amps x 0.1 ohms
Vdrop = 1 volt
P = 1 volt x 10 amps
P = 10 watts
Wait. That is exactly the same formula and answer! Yeah. Nothing in the voltage drop and wire heating formulas gives even the slightest care what the system voltage is. At 600V at the same amps, the wire will heat up the same.
Since heat is the deciding factor in the above tables, they don't care about system voltage either. (It matters only as a percentage; 1 volt drop is a concerning 8% for 12V, a nothingburger 0.8% for 120V, and 0.16% for 600V).
Now you know why Edison lost the war of the currents. Westinghouse could just keep bumping distribution voltage to reduce voltage drop to nothing. Edison couldn't, and had to pay for every inch in copper.
Voltage drop in practice
For example, I have an appliance that requires a 240 volt 15 amp power source. (Its plug is NEMA 6-15.) If I dedicate a circuit to this appliance, which is about 25' from the panel, will 14 AWG be sufficient? Why or why not?
I don't know. Plug it into a Voltage Drop Calculator online and see what you're looking at, and figure out that percentage based on your system voltages. I can tell you this, below 75' for 120V or 150' for 240V, no need to even bother running the calculation, as it will be below any number anyone cares about.
If you're shoveling biblical quantities of power on a regular basis, e.g. a large solar array or an F150 Lightning E-truck, you might bother to do the number-crunch of whether the cost is justified to pay for larger feeder wire. I mean if the bigger wire costs $50 and reduces voltage drop by 1%, you need to buy or sell $5000 of power before that makes sense. Aluminum wire is cheap.
Why do more than the bare minimum?
When 14 gauge wire is appropriate, I've seen 12 used instead. (My home has several circuits like this.) I realize 12 AWG wire may be more difficult to work with, and it costs more than 14 AWG. Beyond these, are there reasons not to do so? Are there any advantages?
The NEC electrical code specifies the absolute slumlord bare minimum beneath which a house is unfit for human habitation.
Some people confuse that for a "best practice".
I think you can see the folly in that thinking.
In practice, 20A circuits where 15A is allowed mean you can run more stuff before the breaker trips. So a heater on high and a PC.
How well does "#14 is cheaper" really work?
There's another reason: The SKU tax. Owning two different kinds of thing is more expensive than owning one. Here, price the following:
- a 250' spool of 12/2
- a 100' spool of 12/2 + 100' of 14/2 + 50' of 14/2.
Wowza! The second one costs twice as much even though it has less copper. So realistically to get sane wire prices, you'll buy
- a 250' spool of 12/2 + a 250' spool of 14/2
Well now, that's a lot of capital tied up, isn't it? That's what I mean by "SKU tax". Your money is tied up from having to own more things. And this out-of-pocket "carrying cost" blows away the theoretical "savings" on #14 being cheaper per-foot. So owning #14 is a net lose for most people.
Obviously it works for builders who wire 3 houses a week, but they buy it by the mile.
I don't own any #14 myself. My smallest wire is #12.