They work the same as long as you don't apply them in 32bit mode in Photoshop.
The way they are applied in Corona is hack of sorts, one I suggested they copy from VFB+ creator by extrapolating the range to avoid clipping the range which LUT naturally does (always).
By applying LUT inside Corona you're basically forgoing true 32bit linear post-production possibility anyway. It's applied in regular gamma space to what you currently see gamma-corrected inside viewport.
This is reason why other softwares like Vray, don't enable baking LUT into 32bit file (if you save .exr with LUT in Vray, the LUT (+ICC) gets ignored.
There really isn't much point to apply LUT to 32bit file in first place as it can't see that information nor output it.