More voltage = more current. More resistance = less current... if you connect the LED without a resistor it will burn-out (maybe even explode).
... on the other hand, you also really don't need to use a car battery to light up a few leds when [8 d-cells] will handle the load.
Go back to the good old water analogy ...Think of voltage as like pressure acting on charge, current is the flow of charge.
... there exist old non-regulated wallwart style supplies ... you should always measure the output voltage with no load ....
one thing to remember as you increase current and accidentally short it out it may melt your wires so gauge the wire size to match current
A good power supply should current limit a little past its rating (e.g. 110 to 130%) without being damaged. That can be used to guard aginst an overload. ... that current limit can be useful for making things more bullet proof.
... Running a supply at the full rating tends to make it run hot ... tends to have more ripple on the supply... I just prefer not to run things close to the limits - I find I have less failures that way
Simple answer: Your circuit will draw as much power as it needs, as long as your power supply can supply enough current. Having excess capability to supply current is not a problem. Your re-think about the wall socket is a good way to comprehend it.
"From what I'm understanding, if you hooked-up an LED straight to the battery it would burn-out but only because the car battery's 12V is about 2x the max input voltage rating of an LED and about 6x what the LED needs in order to light-up. Adding an appropriately sized resistor is important in order to lower the voltage to within the LED's "safe" range. "
Yes, you have it correct (that is just basic math, not calculus).
...you can also see how multiple LEDs in series can 'use' the same 20mA for more efficient use of power.Say 3 in series:(12V - 2.2V - 2.2V - 2.2V)/0.02A = 270 ohmPw = .02 * .02 * 270 = 108mWOnly works when LEDs can be wired in series - for smart LED strips, you need to look at the control chip's datasheet to see how 12V is handled for chips normally powered from 5V.