In line with the Midrash, the Zohar (Vayechi 221a, Emor 105a) seems to say that chavatzelet refers to a younger plant when it is still green and has green petals, while shoshanah refers to a more mature plant that is red and white. That said, Rabbi Daniel Frisch’s Matok M’Dvash interprets this passage Kabbalistically, explaining that that it does not literally refer to colors, but to the progression of Hashem’s mercy: when His Attribute of Justice is first invoked, it is akin to “green” which is pure justice unsweetened by any tint of mercy, while later on His Attribute of Justice appears as a combination of “red” (judgement) and “white” (mercy). Speaking of colors, Peirush Chachmei Tzarfat (to Song of Songs 2:1) explains chavatzelet as a white flower and shoshanah as a red flower.
Another approach identifies the chavatzelet flower as the same as the narkis. That word is a Hebraization of the Arabic word narjis, which, in turn, comes from the Latin word narcissus (derived from the Greek narkissos), and refers to the flower that we call "daffodil" in English. This approach is apparent from Targum (to Song of Songs 2:1), Ibn Janach’s Sefer HaShorashim in the name of Rav Yehudai Gaon, Rabbi Saadia Gaon’s Tafsir (to Song of Songs 2:1), Kaftor VaFerach (ch. 56) in the name of Rav Hai Gaon, R. Shemaryah b. Elchanan of Cairo (d. 1011) in his commentary to Song of Songs (there), and Ibn Ezra (to Song of Songs there).
If the Latin name narcissus reminds of your neighborhood narcissist, it should. This is because in Greek mythology, Narcissus was a young man known for his extraordinary beauty, but also self-absorbed selfishness. One day, Narcissus caught sight of his own reflection and immediately fell in love with it, not realizing that it was merely an image of himself. He became utterly captivated, unable to tear himself away from his reflection, eventually wasting away and dying by the pool. A flower — the narcissus — bloomed at the spot where Narcissus died. That flower, with its delicate beauty and inclination to grow near water, is believed to symbolize Narcissus's vanity and self-love (for a similar tale in rabbinic literature, see Nedarim 9b).
Indeed, the Talmud (Brachot 43b) mentions something called narkom when discussing the blessings over scented plants, but many commentators (including Sefer He'Aruch) have an alternate reading which uses the word narkis instead. In fact, Rashi (there) even connects the Talmudic term narkom back to the Biblical Hebrew word chavatzelet in Song of Songs.
In codifying the blessings over fragrant flowers, Shulchan Aruch (Orach Chaim §216:9) defines chavatzelet as narkis, but then cites an alternate opinion that defines it as lirio (which is Spanish for “lily”). That latter opinion reflects that of Rabbeinu Yonah (Brachot 31b in the Alfasi pagination). Rabbi Moshe Tedeschi-Ashkenazi writes in Ho’il Moshe (to Song of Songs 2:1) that chavatzelet refers to a flower that grows from an onion, hence the string BET-TZADI-LAMMED (batzel, “onion”) in the middle of the pentaliteral word chavatzelet. But then, he adds a comment in Italian that chavatzelet refers to a “lily” or “hyacinth.”
Interestingly, Rabbi Ernest Klein (no relation) surmises that chavatzlet is somehow related to the Akkadian word habasillatu ("stalk").
The word vered does not appear in Biblical Hebrew, but does already appear in the Mishna (Sheviit 7:6-7, Maasrot 2;5, Shabbat 14:4). In the Targumim, the standard word for rendering shoshanah in Aramaic is actually vered. Additionally, the Zohar (KI Tisa 189b) also seems to equate shoshanah with vered. In Modern Hebrew, the term shoshanah refers to a “lily” (which has six petals), while vered refers to a “rose” (which has five petals). Moreover, in Modern Hebrew, the word varod refers to the color “pink,” and is actually derived from the Rabbinic Hebrew term vered.
Rabbi Eliyahu Bachur in Sefer Tishbi cites those who explain shoshanah as referring to a “white lily” with six petals (as in Modern Hebrew), but rejects that approach because there are no thorns that grow with a lily like there are with a rose, yet – as mentioned above — in Song of Songs the shoshanah is said to be something which grows alongside thorns.
As an aside, Bachur also writes that the Mishnaic word vridin (Chullin 2:1) in reference to the “veins inside an animal’s neck” is derived from the word vered, which likewise refers to something red. Although, Rabbi Yaakov Emden (in his glosses Ezer Ohr to Sefer Tishbi) finds this connection farfetched.
Ibn Ezra (to Song of Songs 2:1) cites some commentators as explaining that chavatzelet means vered, and also cites some commentators who explain that shoshanah means vered. If taken together, this might echo the understanding cited above that chavatzelet and shoshanah are one and the same.
In discussing the laws of blessings over fragrant plants, Maimonides (Laws of Brachot 9:6) discusses the shoshanah, narkis (chavatzelet), and vered separately. To Rabbi Yosef Karo (Kesef Mishna there), this implies that those three terms refer to three different types of flowers, which leads him to wonder if vered and shoshanah are not the same thing, then what is a shoshanah?
In clarifying this question, Rabbi Massoud Chai Rokach writes in Maaseh Rokeach that Rabbi Karo knew that both vered and shoshanah refer to “roses” and that one refers to a red rose while the other refers to a white rose, his only question was which term refers to which color of rose (see Maimonides’ commentary to the Mishnah Sheviit 7:6).
Alternatively, Rabbi Yirmiyahu Low (Divrei Yirmiyahu) explains that vered is a general term that can include various types of flowers, while shoshanah is a more specific term that refers to the “rose” as a type of vered. This is borne out in the rabbinic phrase used in Vayikra Rabbah (§23:3) shoshanah achat shel vered (literally, "a single shoshanah of the vered"), which implies that a shoshanah is a type of vered. Alternatively, we may explain that vered refers to the whole plant, while shoshanah refers specifically to the flower.
Where does the Mishnaic/Aramaic word vered come from? Rabbi Ernest Klein (no relation) traces it to the Aramaic word varda (or vardina in some dialects of Aramaic), which he sees as a loanword from the Old Iranian wrda. He explains that latter word as the etymon of the Greek rodon and the Latin rosa, such that the English word rose (which derives from the Latin) is actually etymologically-related to vered!
