When I first heard, or rather read, "discrete" - it must have been in the 1960s or 70s - it was in an academic context and specifically that of language study or linguistics. Even then I wondered , I am pretty sure, if it added anything to "separate". But it did: it added a certain "cachet". Or would that now be spelt "caché"? (Btw, you will sometimes hear "a caché of weapons", nowadays.)
Recently the spelling is showing signs of taking over from "discreet", defined in my Collins Cobuild as "careful to avoid embarrassment". (The pronunciation has not changed, and so remains the same for both, as far as I have observed. ) Those who use it like this, I would have been tempted to say, give themselves away: they cannot be real writers, or even readers, certainly not of quality or academic material. That now sounds a very snobbish thing to say. I apologise. You read it (when you might have expected "discreet") in the "quality press" and on websites that should know better (oops, sorry again).
But, talking of snobbery, is it not part of what you might call the trend towards "the posh option"? Those trying to impress use what they take to be a posher, a more distinguished word? It might be "word inflation", where a longer word is used, a syllable added, "competency" for "competence", for example. Or it might be that "fulsome" is thought to be a more substantial version of the rather plain "full". Or maybe a certain spelling is seen to be, as here, more learned. Of course, spellchecking and autocorrecting software creates further confusion with apparently authoritative but in reality, foolish and literally (ie in fact) brainless suggestions.
I am not, of course, talking about long-established forms such as "transportation", even where "transport" is perfectly adequate. This is now used by UK local authorities, I suppose, for its sonorous effects. I have given up saying silly things like, "Surely we don't want to revive the penal colonies?"
By the way (btw, earlier, sorry again), there is a subtle little joke about this in Patrick O'Brian's "Desolation Island". Aubrey is outraged that his new command, "the horrible old Leopard", is to be used for transportation. Is that not the prime purpose of a ship, asks Maturin, in apparent innocence.