Although colloquially translated as "offspring," the term "zera" carries specific connotations in the lexicon of Chazal. Tosafos (Yevamos 22b, s.v. "Ben") contrast the term "zera" with the term "ben" - son. While "ben" can refer to any child, "zera" specifically denotes offspring of pure Jewish lineage. Furthermore, while the term "ben" includes only first- generation descendants, the term "zera" includes all future generations as well.
The Gemarah itself expresses this distinction as well. In Meseches Sanhedrin (59b), the Gemarah derives that the mitzvah of bris milah applies only to the descendants of Yitzchak, but not to the descendants of Yishmael, from the possuk: "Va'ata es brisi tishmor, v'zar'acha acharecha l'dorosum - and as for you, you shall keep my covenant, you and your offspring after you throughout their generations" (Bereshis 17:9). The Gemarah reasons that bnei Yishmael could not possibly be included in this commandment, because the term "zera" refers specifically to the descendants of Yitzchak, as the Torah states, "Ki b'Yitzchak yikarei l'cha zerah - since through Yitzchak will offspring be considered yours" (Bereishis 221:12).
The Rambam (Peirush HaMishnayos Nedarim 3:9) proffers a further proof in support of the specific connotation of "zera," the Rambam notes that HaKadosh Baruch Hu promised serious suffering to Avraham's "zera"- "Yadoa teida ki geir yehiye zaracha b'eretz lo lahem v'avadum v'inu osam arbah me'os shanah - know with certainty that your offspring shall be aliens in a land not their own, they will serve them, and they will oppress them, four hundred years" (Bereishis 15:13), but the Torah teaches that the descendants of Yishmael and Eisav settled in their lands with ease and comfort. Because only Bnei Yisrael suffered in a foreign land before attaining salvation, only Bnei Yisrael were included in the possuk's promise to Avraham's "zera."
The Rambam's explanation provides additional insight into the meaningful passage we recite at the Pesach Seder: "V'arbe es zar'o v'etain lo es Yitzchak. V'etain l'Yitzchok es Yaakov v'es Eisav, v'etain l'Eisav es Har Seier lareshes oso, v'Yaakov u'vanav yardu Mitzrayim - I multiplied his family and gave him Yitzchak. To Yitzchak I gave Yaakov and Eisav; to Eisav I gave Mount Seir to inherit, however Yaakov and his children went down to Eygpt."
It was precisely through Bnei Yisrael's suffering in the foreign Mitzrayim, in contrast to the tranquility and immediate success enjoyed by the descendants of Eisav, that Bnei Yisrael confirmed their status as the true "zera" of Avraham Avinu.