We know they are different but the vexed question - with controversy inbuilt - is 'Do WAVs and FLACs sound different?'
The moment we move the discussion to 'do they measure differently?', we're into a whole other domain of trouble. Who's measurements? Which measurements? Where? How? With what equipment?
Especially when seeking something as subtle as this gremlin, the devil is really in the detail. A half-assed attempt at it is worse than none at all because it generates spurious, but authentic-looking, data. If issues like this could be settled with commonly available techniques, all such debates wouldn't everywhere rumble on. I would be quite surprised if all these different boxes turned out to be as identical as the measurements suggest.
With lenses, there's a similar issue: on one level, a lens is simple: all it does is bend light: it comes in one end and exits the other. What's the fuss? But there is inevitable transmission loss, expressed as Modulated Transfer Function.
Manufacturers publish MTF charts that appear to be a complete description of how that lens resolves. But . . . each manufacturer has a slightly different methodology and way of communicating the results, so it's not possible to compare a Nikon lens with a Canon one exactly. Two or three different frequencies are sampled, leaving crucial gaps unmeasured. Then, there are question marks over sample variation: the test results are only valid for that lens: the one you buy will almost certainly not give exactly the same performance. And anyway, how exactly does that squiggly line on the chart translate to actual performance? The MTF data is absolutely truthful within a tiny band of usefulness.
Other losses are measured: geometric distortion and various types of chromatic aberration are mapped very precisely, though of course with slightly incompatible measurement systems, and rarely full spectrum. With all this data, do we finally know how the lens draws a picture? No.
Because the eye/brain is sensitive to all kinds of crucial stuff they don't, won't or can't measure: rendition of defocused areas, and the transition between focus and defocused zones is critical to the 'look' of the image. Not measured. Microcontrast and macrocontrast behaviour isn't usually evident from the published data. Different lenses have different depth of field effects at the same aperture. They are differently prone to flare and ghosting: again, no measurements available. Each lens renders colours differently but again you don't find measurements for that. There may be further 'intangibles' that comprise the 'signature' or 'character' of a lens even less susceptible to description or reductive analysis.
The bottom line is you just shoot with it and check the results.
Fortunately, the results can be digitally captured 'asynchronously' and examined at leisure. Here's the final rub, though: the inspection of the lens is limited by the resolution and characteristics of the imaging system. In audio equivalence, the ear/brain is an entirely different kind of 'imager' to an ADC, and the 'experience' can't be recorded with a PET scanner and better interpretative neurology than we currently have.
Fascinating though the attempt is, there may always be a gap between what is commonly measured and what we hear. Our mind may or may not prove to be an unreliable witness.
The problem with mechanical measurements is the noise floor - what's +N? - the scope and quality of measurements made, and interpretation of the data. The problem with listening is 'reporting' and our gullibility. Nothing's perfect.