Everyone eats "shmura" (guarded) matza. The question arises at what point the wheat or the flour must be guarded to ensure that it has not become wet and possibly turned into chametz. Once someone determines that they are following a particular level of shimur, then they can determine if they will or will not eat "gebrochts" because of the possibility that some flour was not cooked enough and can become chametz.
These are two different problems and are treated completely independently.
The three levels of shimur are
WHEN DOES SHIMUR START?
There are three opinions discussed in Halacha as to the level of
guarding that is required. The most lenient opinion states that this
requirement is satisfied as long as care is exercised from the time
the flour is mixed with water to ensure that the matzah is baked
before it can become chometz (Shmurah mi’Sh’as Lisha). This approach
is based on the assumption that flour is generally stored away from
water, and chometz concerns only begin at the point of kneading the
dough, where water is added to the flour. This opinion, however,
should only be followed in cases of extreme necessity, and none of the
matzah sold today follows this approach. [Indeed, most wheat today is
soaked (tempered) in water before milling, which raises the concern
that it may be true chometz].
The second opinion holds that the grain must be guarded from the time
it is milled into flour. This approach is based on the assumption that
whole grains are not susceptible to becoming chometz even if they were
to become wet, since the hard, unbroken kernels are normally resistant
to water. Once milled, however, the grains lose this protected status,
especially where flour mills were powered by running water and the
flour was thus exposed to moisture. Such flour is called Shmurah
mi’Sh’as Techina. The grain is inspected before milling to ensure that
it has not begun to sprout or exhibit other signs of chimutz, and by
doing so we are assured that even if the whole grain had become wet it
had nevertheless not become chometz. Most machinemade matzah uses such
flour, and such matzah is commonly referred to as matzah
p’shutah—“regular matzah”.
The third approach requires supervision of the grain from the time of
its harvesting until the actual baking of the matzah to ensure that it
did not come into any contact with water at any point whatsoever prior
to making it into a dough. This approach is concerned that the kernels
may have cracked after harvesting and become wet, creating a chometz
concern. Indeed, care is taken to harvest the grain before it is fully
ripe, since fullyripened grain—even if still on the stalk—could
potentially become chometz under the right conditions. There is even a
discussion in the Poskim about whether a Jew must actually harvest the
grain, and whether one must supervise the transport of the grain to
ensure that it does not come in contact with water! Flour that is
“guarded” to this extent is known as Shmurah mi’Sh’as K’tzirah, and
this is the flour that is used to bake all hand and some machine
matzah. Such matzah is referred to as “Shmurah Matzah,” although all
other matzah is also, technically, “shmurah” according to many
opinions.