I mistyped, 1156 are single, and 1157 are dual
That is how 1157's work.
Bulbs don't change based on voltage, as the voltage should always be 12v.
The 1157 have two inputs, one input is for 5w brightness, and the other input is for 21w brightness. Depending on what wire has power depends on how bright it is (like your headlight bulb). Except normally on these the low power one stays on all the time unlike your headlight.
The 5w input is used for your running lights, or tail light. the 21w input is used for turn signals and brake light.
Depending on the LED you use, if it's single color, it will work the same exact way as above.
If your using a switchback led, that means it will change color depending on the input, and normally (I haven't seen any) not change brightness, both inputs will be full brightness. So you wouldn't use a switchback led on your brake light.
But using a switchback led on a turnsignal light means the normal low power amber running lights you have on the front will now be full brightness white, and when you use your turn signals they will change to full bright blinking yellow.
Ones like this one will either adjust the led voltage, or only light some of the leds on low, and use full voltage or power all the leds on high brightness. LED's normally run in the 1-3volts range, so they always have to convert it in the bulb from 12v.
These will run full brightnes on both low and high, except low is white, and high is amber (turn signals).
Be careful when changing out your turn signals with LED though. You need to make adjustments or replace your flasher unit with an electronic flasher, and maybe add diodes to your turn signal indicator.
Some LED's only power one way, and you have to flip them if they don't light (1156/1157 you cant flip, but like the car reverse/turn light ones, T10's) you will probably be fine.
If your LED is nicer and works both ways (they have diodes in it to idiot proof it), then your your likely get 4way flash on all your turn lights.
Sorry, I misunderstood, that brake controller gives tail light to the turn signals using lower voltage.