Sex: biological categories based off of reproductive organs
Gender: sociological and cultural categories
Cis: your sex and gender align, i.e. I am cis, I am a cis-woman.
Trans: your gender does not match your sex, i.e. I am trans, I am a trans-male (I was born a biological woman but am a man)
Intersex: people who do not fit the typical definitions for male or female bodies due to variations in sexual characteristics e.g. chromosomes, hormones, reproductive organs
(א) אַנְדְּרוֹגִינוֹס יֵשׁ בּוֹ דְּרָכִים שָׁוֶה לַאֲנָשִׁים, וְיֵשׁ בּוֹ דְּרָכִים שָׁוֶה לַנָּשִׁים, וְיֵשׁ בּוֹ דְּרָכִים שָׁוֶה לַאֲנָשִׁים וְנָשִׁים, וְיֵשׁ בּוֹ דְּרָכִים אֵינוֹ שָׁוֶה לֹא לַאֲנָשִׁים וְלֹא לַנָּשִׁים:
(ה) כֵּיצַד אֵינוֹ שָׁוֶה לֹא לַאֲנָשִׁים וְלֹא לַנָּשִׁים: אֵין חַיָּבִים לֹא עַל מַכָּתוֹ וְלֹא עַל קִלְלָתוֹ לֹא כַּאֲנָשִׁים וְלֹא כַּנָּשִׁים, וְאֵינוֹ נֶעֱרָךְ לֹא כַּאֲנָשִׁים וְלֹא כַּנָּשִׁים, וְאִם אָמַר "הֲרֵינִי נָזִיר שֶׁזֶּה לֹא אִישׁ וְלֹא אִשָּׁה" אֵינוֹ נָזִיר. רַבִּי מֵאִיר אוֹמֵר: אַנְדְּרוֹגִינוֹס בְּרִיָּה בִּפְנֵי עַצְמָהּ הוּא וְלֹא יָכְלוּ חֲכָמִים לְהַכְרִיעַ עָלָיו אִם הוּא אִישׁ אוֹ אִשָּׁה. אֲבָל טֻמְטוּם אֵינוֹ כֵּן, פְּעָמִים שֶׁהוּא אִישׁ פְּעָמִים שֶׁהוּא אִשָּׁה:
(1) The androgynous is in some ways like men, and in other ways like women. In other ways he is like men and women, and in others he is like neither men nor women.
(5) ... Rabbi Yose says: the androgynous is a unique creature, and the sages could not decide about him. But this is not so with a tumtum (one of doubtful), for sometimes he is a man and sometimes he is a woman.
Androgynous = both sexual organs (what we today call intersex)
Tumtum = ambiguous/recessed sexual organs
(א) וַיֹּאמֶר אֱלֹהִים נַעֲשֶׂה אָדָם בְּצַלְמֵנוּ כִּדְמוּתֵנוּ (בראשית א, כו), רַבִּי יוֹחָנָן פָּתַח (תהלים קלט, ה): אָחוֹר וָקֶדֶם צַרְתָּנִי וגו'
(1) ... Said R’ Yirmiyah ben Elazar: In the hour when the Holy One created the first human, He created him [as] an androgyne/androginos, as it is said, “male and female He created them”.
Is a prayer in that case ineffective? Rav Yosef raises an objection based on a baraita: It is stated: “And afterwards she bore a daughter, and called her name Dina” (Genesis 30:21). The Gemara asks: What is meant by the addition of the word: Afterwards? What does the verse seek to convey by emphasizing that after the birth of Zebulun she gave birth to Dina? Rav said: After Leah passed judgment on herself and said: Twelve tribes are destined to descend from Jacob, six came from me and four from the maidservants, that is ten, and if this fetus is male, my sister Rachel will not even be the equivalent of one the maidservants; immediately the fetus was transformed into a daughter, as it is stated: And she called her name Dina; meaning she named her after her judgment [din]. The Gemara rejects this: One does not mention miraculous acts to teach general halakha.
(ח) פָּתַח רַבִּי שִׁמְעוֹן וְאָמַר (בראשית יג) וַיֵּלֶךְ לְמַסָּעָיו מִנֶּגֶב וְעַד בֵּית אֵל עַד הַמָּקוֹם אֲשֶׁר הָיָה שָׁם אָהֳלֹה בַּתְּחִלָּה בֵּין בֵּית אֵל וּבֵין הָעָי. וַיֵּלֶךְ לְמַסָּעָיו, לְמַסָּעוֹ מִבָּעֵי לֵיהּ. מַאי לְמַסָּעָיו. אֶלָּא תְּרֵין מַטְלָנִין אִנּוּן. חַד דִּידֵיהּ וְחַד דִּשְׁכִינְתָּא. דְּהָא כָּל בַּר נָשׁ בָּעֵי לְאִשְׁתַּכְּחָא דְּכַר וְנוּקְבָא בְּגִין לְאַתְקָפָא מְהֵימְנוּתָא. וּכְדֵין שְׁכִינְתָּא לָא אִתְפָּרְשָׁא מִנֵּיהּ לְעָלְמִין.
(8) Then Rabbi Simeon said: "It is written, 'and he went on his journeys from the south to Bethel unto the place where his tent had been at the beginning, between Bethel and Hai' (Gen. 13:3). It says, 'He went on his journeys' instead of 'his journey.' Why is that? There is a reference not only to his own journeying, but also that of the Schekina, who always went with Jacob, and therefore we learn that every person needs to be male and female at all time, for the sake of his faith, he ought not to think or imagine that the Schekina forsakes