There is a custom(?) to abstain from eating matza 30 days before Passover so that the taste will be new. There are some sects of sefardic or teimani Jews who eat a type of matzah that is more akin to the lafa bread used to wrap shwarma or falafel. Do those who eat this kind of matzah similarly abstain from eating breads like pita or lafa 30 days before Pesach so that the taste is new to them?
The basis of the prohibition of eating matzah on erev Pesach (which was later expanded to longer periods before Pesach) may be found in Yerushalmi Pesachim 68b:
The idea appears to be that one is spoiling one's taste for matzah by having it just before the appropriate time.
People attribute the following quip to Achad HaAm, but I've heard that it was really Bialik; I've also seen it attributed to Smolenskin:
Nowadays we have chametzdik matzah available year-round. I would guess that the minhag does / should encompass such chametzdik matzah, since it would spoil one's taste. But a flat chametzdik cracker would not fall under this custom.
In terms of laffa and soft matzah, I can echo the quip: I've tried both and they are not the same. Laffa tastes good. Soft matzah does not. It is just awful. No one would confuse the two.
(It is perhaps slightly better if you take it right out of the oven just then.) Our crisp matzah is 100 times better.
The prohibition of eating matzah on erev Peasach (and therefore the extended customs) only applies to matzah which can be used for the mitzvah (see Egg matzah in early Nisan).
Therefore, it appears that laffa would be permitted since it not only can't be used for the mitzvah, but is actual chametz.