The foundation of honoring parents rests on the concept of partnership in creation: Kiddushin 30b teaches that God, the father, and the mother are three partners in forming a person, and when a child honors his parents God counts it as though He Himself were honored — a theological grounding that explains why the obligation is so weighty.
The Gemara defines both the positive acts of honor (feeding, clothing, escorting) and the obligations of reverence (not sitting in a parent's place, not contradicting them) in Kiddushin 31b, and Mishneh Torah, Rebels 6:3 codifies that these duties of honor are performed from the parent's own funds when available, and from the child's when not — a framework carried into Shulchan Arukh, Yoreh De'ah 240:5 and elaborated upon by Chayyei Adam 67:4, who adds that even providing for parents lavishly while showing a sullen face incurs punishment, while serving them in hardship with kind words and good intent earns a share in the World to Come.
The honor owed to a stepparent is a distinct, Torah-derived obligation: Arukh HaShulchan, Yoreh De'ah 240:43 rules explicitly that one is obligated to honor one's father's wife even though she is not one's mother, and to honor one's mother's husband, deriving this from the Gemara in Ketubot — 'Honor your father' includes the father's wife, and 'your mother' includes the mother's husband — and Beit Yosef, Yoreh De'ah 240:35 traces this to the same source, noting further that Rabbeinu HaKadosh instructed his sons to maintain honor for his wife even after his death, though she was not their mother.
This obligation to honor a stepparent is temporally bounded: Tur, Yoreh De'ah 240 rules that the duty to honor a father's wife or a mother's husband applies only while that parent is alive, and lapses after death — though it remains a praiseworthy practice to continue honoring them even thereafter, and Arukh HaShulchan, Yoreh De'ah 240:43 confirms that all God-fearing people maintained this custom.
The Sefer Charedim extends the honor due to stepparents to active physical expressions: Sefer Charedim, Positive Commandments 6:2 holds that obligations of rising before one's grandfather and grandmother, one's mother's husband, and one's father's wife all apply, and that when a parent dispatches one on an errand of religious significance one should run with alacrity.
When the honor of a biological parent and the honor of a stepparent conflict, the biological parent takes precedence: Kiddushin 31a records that Rabbi Eliezer ruled that when both parents call for water simultaneously, a child sets aside the mother's honor to attend to the father, because both the child and the mother share an obligation to honor the father — illustrating the principle that the party to whom more people owe a duty takes priority.
The limit of all parental honor, biological or otherwise, is the service of God: Yevamot 6a and Yevamot 5b both cite the baraita that one might have thought honoring father and mother overrides Shabbat, but the verse 'You shall fear each man his mother and his father and keep My Shabbatot' teaches that all parties — parent and child alike — are obligated in God's honor, and Rashi on Vayikra 19:3 sharpens this: 'You and your father are both obligated in My honor; therefore do not obey him to annul My words.'
Mishneh Halachos 4:167 concludes, on our reading of the cited page, that while raising and educating another's child is a tremendous merit homiletically equated to giving birth, the adoptive relationship does not erase biological lineage — the child owes immense gratitude and respect to adoptive parents, but biological identity must not be falsified — and Mishneh Halachos 4:170 concludes, on our reading of the cited page, that concealing from an adopted child the truth of their biological parentage is strictly forbidden on account of numerous serious halachic complications including prohibitions of yichud, errors in levirate marriage, lineage status, inheritance, and mourning, ruling that adoptive parents are obligated to disclose the biological truth.