From a careful reading of the Chumash one realizes the dual nature of the night of the 15th of Nissan. First, it is חג הפסח, a one-day holiday that begins on the morning of the 14th and ends that night. This night is also the beginning of חג המצות, a seven-day holiday. The important Mitzva of חג הפסח is the Korban Pesach, which we are commanded to eat roasted, with Matza and Maror: צלי אש ומצות על מררים יאכלוהו (Shemot 12:8). The central Mitzva of חג המצות is eating Matza: בארבעה עשר יום לחדש בערב תאכלו מצות (Shemot 12:18).
One practical ramification of this distinction is that since the Mitzva of Korban Pesach cannot be fulfilled nowadays, the Matza and Maror that we are to eat with the Korban Pesach are no longer obligatory, as the Matza and Maror as recorded in Shemot 12:8 are only complements to the Korban Pesach. However, the Mitzva of eating Matza on חג המצות (as commanded in Shemot 12:18) is unaffected by the absence of the Korban. It is for this reason that most Rishonim believe that the obligation to eat Matza is still a biblical obligation while the obligation to eat Maror is only rabbinic in nature.
This distinction can also explain a difficulty in Parshat Beha’alotcha. One year after Yetziat Mitzrayim, Hashem commands Moshe to tell Bnai Yisrael to bring the Korban Pesach. Why is a special reminder needed if the Mitzva of Korban Pesach is given in Shemot 12-13? Because Shemot 12:14 states that חג המצות is לדורותיכם, for future generations, while 13:5 states: והיה כי יביאך ה' אל ארץ הכנעני…ועבדת את העבודה הזאת. The Korban Pesach is only to be brought once Bnai Yisrael enter Eretz Yisrael.
When this command is given, this distinction seems meaningless as Bnai Yisrael are leaving Mitzrayim and are to go from Mitzrayim to Har Sinai, receive the Torah then travel straight to Eretz Yisrael. Because of חטא העגל, though, Bnai Yisrael’s trip was delayed by several months. It is during this delay that the distinction between לדורותיכם and כי יביאך ה' אל ארץ הכנעני becomes a practical one. Hashem therefore tells Moshe that the Korban Pesach is to be brought this year as well.
This story is the introduction to Pesach Sheni, the makeup opportunity granted to those who were unable to bring the Korban Pesach in Nissan. It is not the seven-day חג המצות that one can make up, just the one-day חג הפסח. While there is no separate Mitzva to eat Matza or to abstain from Chametz (as these are Mitzvot of חג המצות, the Korban itself cannot be eaten with Chametz and is eaten with Matza and Maror (על מצות ומררים יאכלהו, Bemidbar Sinai 9:11). One who is not bringing a Korban on Pesach Sheni has no obligations on that day regarding Matza or Maror.
The two holidays, חג הפסח and חג המצות overlap by several hours. While we are sitting at the Seder this year, we should recognize that while we are celebrating חג המצות through our consumption of Matza and observance of the day as a יום טוב (albeit without the קרבן חגיגה) we are unable to perform the central Mitzva of חג הפסח.