Is there a difference between A=432 and A=440? Most definitely. A difference of 8Hz at that particular A. A noticeable emotional or other difference in the music as far as a listener or musician is concerned? I doubt it, and if there is then anyone so afflicted should probably stay away from strings, guitars, brass, most woodwind, analogue synths etc. because those instruments rarely produce exactly the same pitch for any given note twice in a row. Fretted string instruments are impossible to intonate so that every note is exact, and fretless are at the mercy of tiny shifts in finger placement and pick/bow use by the player.
Once upon a time A=454 was common. The last users of A=454 were the Salvation Army brass and concertina bands, who gradually abandoned it when brass instrument manufacturers decided to cease making A=454 instruments around the end of the 19th century. So modern brass and military bands who play music from before c.1900 are playing slightly flat compared to their predecessors
Does it matter? Not much.
One reason for guitarists tuning down that doesn't seem to get mentioned much has nothing to do with A=anything. It's because some keys and chord shapes on the guitar allow a guitarist to play stuff they can't so easily in other keys, or even play at all. The same reason for using capos really. So if the riff works best played using the first position E chord fingering for example, but the singer can't comfortably get the high notes in E but can in D tuning the guitar and bass down a tone solves the problem.
It also makes heavier strings much easier to vibrato and bend and vibrato (or tremolo as Leo Fender misnamed it) bridge setups like the Bigsby and Strat systems easier to set up and operate.