As promised:
There are THREE (really four) different aspects of what is known as “Tznius” (which is like calling lighting a fire on shabbos “Mukzta”). They are:
1: Ervah
2: Das Moshe/Yehudis
3: Tznius
4: Histaklus
1: Ervah is a din in Kriyas Shema (which is why the halchos are in Keriyas Shema). Many Rishonim hold it applies to other brachos as well. The idea is that a Davar Sheb’kedusha may not be done/said before any Ervah. That includes for a man (as per the Gemorah Brachos) a woman’s hair, shok, etc. This has NOTHING to do with the general idea of a man looking at a lady. See Shulchan Aruch, Orach Chaim 75 for more details.
2: Das Moshe/Yehudis is what the Torah perscribes that a female should not have uncovered when she goes out in public. This includes hair of anyone who is not a Besulah (as per Even HaEzer 21:2). The Mishna in Kesubos (72B) differentiates between the two. Ayin Shom. (Rav Moshe IIRC also has some teshuvos on the matter).
3: Tznius: There is a general concept of Hatznya Leches. This applies to both males & females, both in manner of dress and action, to be “low-key”. (There are also halachos of Tnzius in OC 240, which I will ignore for this discussion). An example is a woman covering her hair in her own yard (a private domain), where there is no Chiyuv (seemingly even if others will see her), but there is a concept of “Tznius”. (Offen a Bais Shemuel in Even HaEzer). In general, Chassidim are more Machmir in this.
4: Histaklus: A man may not stare at a woman. Period. If he does, he is Over “Lo Tasuru”. It certainly is a good thing for women to make sure that men have no reason to stare at them, but unless it is “Trai Ivri Nahara”, then it is not “Lifnei Iver”.
I hope this clears things up. This is from memory & is not fully comprehensive, so if you have sources that I missed, you are probably correct.