The Gemara explains that both for Pesach Mitzrayim and Pesach Doros, the
obligation to eat the Korban Pesach applies only one night. However, what
the Mishnah means is that the Isur of Chametz during Pesach Mitzrayim
applied during the first night *and day*, while the Isur of Chametz of
Pesach Doros applies all seven days.
If Chametz was Asur for both the night and the day during Pesach Mitzrayim,
why does the Torah say that the dough which the Jewish people took with them
was baked into Matzos because "they were rushed out of Mitzrayim and did not
have time to make it into bread (Shemos 12:39)?" Even if they were not
rushed out, they could not have made bread because Chametz was Asur for them
during that day! Why does the Torah imply that they would they have made it
into bread had they not been rushed out?
(a) The RAMBAN (Shemos 12:39) explains that they certainly would not have
baked Chametz, even had they not been rushed. The point of the verse in the
Torah is not to teach that had they not been rushed, they would have baked
bread. Rather, it is teaching that had they not been rushed, they would have
baked Matzah *at home in Mitzrayim*, and not while traveling. The Torah is
telling us that they baked the dough as they traveled because they were
rushed out (and that is why it was still dough and not a finished product of
Matzah). The Torah is emphasizing that they baked it on the road and not in
Mitzrayim.
In a similar vein, the DA'AS ZEKENIM explains that when the Torah says that
the Jewish people were rushed out of Mitzrayim, it is not explaining why
their dough was made into Matzah and not Chametz. It was Asur to have
Chametz, as our Gemara implies. Rather, the verse is explaining why the
*only item* of food that they brought with them was dough and nothing else -
- "[because they were rushed out] they did not have time to prepare other
provisions for themselves."
(b) The RAN (25b of the Rif) says that although there was an Isur to *eat*
Chametz during Pesach Mitzrayim, there was no Isur to *own* Chametz (Bal
Yera'eh and Bal Yimatzei). They were baking bread to eat on the following
day (since the prohibition of Chametz applied for only one day that year),
and it was permitted for them to be in possession of it during the day of
Pesach. (See TZELACH, Pesachim 116b, who challenges the Ran's explanation.)
(c) The HAFLA'AH (Panim Yafos, Bereishis 8:22, Bamidbar 33:3) writes that
before Matan Torah, the definition of 'day' for Jews and non-Jews was alike
-- the night followed the day, instead of the night coming first (as it does
in all present-day matters of Halachah). Based on this idea, it may be
explained that when the Gemara says that it was forbidden to have Chametz
for one full day, that meant the day of the *fourteenth* of Nisan (when the
Korban Pesach was slaughtered) and the night following that day. But on the
day on which they actually left Mitzrayim (the fifteenth) there was no Isur
of Chametz at all! (Heard from Rav Kalman Weinreb in the name of Rav Dovid
Kronglass, zt'l.)
According to this explanation, the Mishnah -- which says that during Pesach
Mitzrayim the Isur of Chametz applied for one night -- does not contradict
the explanation of the Gemara which says that it means a whole day (day and
night). When the Mishnah says "one night" it means the time of the Isur of
Chametz which is common with Pesach Doros -- is only one night -- the first
night. The Mishnah does not discuss the day before that night, since that is
not common with Pesach Doros, because it was the day before Pesach.
The TZELACH (Pesachim 116b) in fact suggests a similar explanation to the
above, positing that when referring to Pesach Mitzrayim, "one day" refers to
a day *followed by* the night. However, he gives a different reason for
defining a 'day' in this manner. The verse (Shemos 13:4) which our Gemara
brings as the source for the Isur of Chametz during Pesach Mitzrayim is
written in a discussion of the Avodas Korban ha'Pesach (Shemos 13:5, Rashi
there). When it comes to Kodshim, the night follows the day (Chulin 83a).
Hence, the Isur of Chametz which is written in proximity to a discussion of
the Korban Pesach is referring to a "Kodshim-day," which begins with the
daytime *followed by* the night.