On the iPhone, the built in photo lighting adjustments includes exposure, brightness, and brilliance. They are all slightly varied settings, but it's hard to really tell what's exactly going on. What is different about these settings that makes each one unique?
Not an answer because I don't know details of the iPhone, but there are four ways (four to my knowledge) to "brighten" an existing image.
Most usual Brightness sliders in photo editors simply slide all the data up by adding a given constant to all pixels. If you go very far, this can of course heavily clip data at 255. Not the best way. If you add 30, then 0 becomes 30 (not black) and 255 becomes clipped by 30.
Much better is to adjust gamma, for example, the Center slider in Adobe Levels. Gamma has the property of fixing both end points, they cannot possibly move, so you can brighten the dickens in one with zero risk of clipping. Also meaning no dynamic range change, just brighter.
The White Point in Levels is a very common method (is also the Exposure slider in Adobe Camera Raw). It sets a new white point. For example, sliding white point down from 255 to say 220 says to boost the data so that the previous 220 data will become 255. This of course clips anything in between, but that point was visible and studied in the histogram (i.e. it is our choice). Then the adjustment of the rest of the data is a curve not exactly the same as linear exposure, but except at the highest end, it's probably within 1/3 stop of a linear change.
The Photoshop menu Images - Adjustments - Exposure has an Exposure slider that adjusts by actually calculating new values for a given linear exposure boost. +1 EV raises all values by +1 EV. This is pretty uncommon. Photoshop offers all of the methods.
A curve tool can mimic 2. and 3.
You could study the changes each iPhone choice performs, and probably figure out which is which. It would seem most important to know what both end points do.