"The Jews had gladness (simcha) and joy (sason)" (Esther 8:16). Simcha is yom tov, as it says "You shall be happy on your holiday" (Devarim 16:14). Sason is milah, as it says "I rejoice over your word" (Tehillim 119:162) (Megila 16b).
Perhaps the nuanced distinction between the two synonyms, simcha and sason, is based on their etymological cognates. In his commentary on Tehillim (14:7), Rabbi S. R. Hirsch links the root of sameach with the word tzemach, flower. A flower blossoms beautifully. Large petals grow on a flower each spring, the peak of vegetative splendor. However, in a fairly short while, the petals fall or wither, their beauty reduced to a cherished, sometimes distant, memory.
By contrast, the root of sason - sas - is related to tzitz, budding. "It brought forth a blossom, it sprouted a bud" (Bamidbar 17:23). The bud may sprout either before or after the blossom, but always lasts much longer and eventually becomes a fruit (Rashi and Sifsei Chachamim).
When the two synonyms are juxtaposed, simcha, like a flower, represents a peak of happiness; it is intense, and, by definition, short-lived [R Hirsch disagrees with this point]. Therefore, simcha refers to yom tov, an intense, but fairly brief, period of happiness.
Sason, like a bud, is much smaller than simcha, a flower, but is much longer lasting. Therefore sason refers to mila, the only mitzvah which endures throughout a man's lifetime. David HaMelech rejoiced over mila, which comforted him in the bathhouse when he was naked of all other mitzvos (Rashi Shabbos 130a, based on Menachos 43b). Moreover, mila, which was accepted with joy, is still performed with joy (Shabbos 130a).
When Adar begins, we increase simcha (Taanis 29a). Purim and Pesach are highlights of the Jewish calendar, celebrating great miracles (Rashi) with peaks of happiness. As we enter Adar and increase simcha, we must also focus on sason, the more muted and enduring type of joy. In fact, the gemara (Shabbos 88a) understands, based on "kiymu v'kiblu haYehudim" (Esther 9:27), that Purim is a day of kabbolas haTorah. On Purim the Jews joyfully accepted the Torah without the coercion that was present at Sinai. The joy of accepting and learning Torah uniquely combines the intensity of simcha and the enduring nature of sason. Thus this season is a perfect time to recommit ourselves to learning Torah.
In every province and in every city, the Jews had gladness and joy (Esther 8:17). Kain tihye lanu - so may it be for us.