What brought me to inquire about this topic (besides seeing products as being labeled not kosher for Pesach) was the name Matzah itself. Matzah by definition means unleavened bread. I understand that when things are done intentionally for The Creator you would (should) give a Terumah or your best willfully but it still didn't make sense to me how you can have Matzah, that's not really Matzah. Doing further research I came across articles (here, here, here) but what really stood out to me was this article and the author use of the word "opinion". Even further research seeing Rabbi Akiva's argument/assertion/thoughts on the matter here. Outside of taking the leaven out of one's household Shemoth/Exodus 12:17 and Devarim/Deuteronomy 16:3 makes mention of eating and guarding the Matzah in remembrance as a Zikron/Memorial and a Khag/Feast of the liberation. My question is why are some Matzah labeled as not being kosher for Pesach/Passover when the Torah plainly states to eat unleavened bread?
It's not for Passover!
Some people feel like having matza-like crackers the rest of the year, so some matza companies said -- hey, let's make more of our stuff, but we don't have to be careful about baking it so fast, or keeping the flour dry in advance, or all that complicated stuff. Hence, "not for Passover matza", which yes, technically is not "matza" in a literal sense.
Don't eat it on Passover.
The pasuk says ושמרתם את המצות, guard the matzos. From here we see that matzoh needs supervision that it does not become chometz. Matzoh that was not supervised like that can not be recommended for eating on Passover and may not be used at the Seder under any circumstances. It could be chometz, even though it most likely it isn't.
This makes a difference. On the day before Passover one is not allowed to eat matzoh, and that should include unsupervised matzoh. However, matzoh produced specifically not for Passover is not included in the prohibition according to some opinions.