Both 失恋する and 振る mean to be rejected. But then are they exactly the same thing? What are the nuances between those two words?
Thank you in advance.
As istrasci noted in the comments, 振る (in relation to romance) means "to reject". In physical terms, it literally means "to shake" or "to wave", and the romantic meanings could thus be understood as similar to the English phrasing "to shake or wave someone off" → "to get rid of someone, to reject someone".
Looking at this second term, the individual kanji mean "to lose" + "love (especially passionate or carnal love)".
Idiomatically, it's more like "to lose in love", as in, "to love someone but not get anywhere with them" → with connotations of either unrequited love, or rejected love.
I've struck out text above due to a misapprehension on my part, due in part to misleading reference materials. After chatting some with native speakers here and earlier, and also offline, it turns out the meaning of 失恋する is much closer to the literal spelling: forget about "unrequited love", a better English gloss would be "to become broken-hearted".
振る then is what the rejecter does, while 失恋する is what the person in love with the rejecter does.
An example (albeit somewhat forced):
Because that girl turned him down, he became broken-hearted.
Note the "became": the Japanese term refers to the change of state from in love to broken-hearted. I've changed the usage example above accordingly. Using a -ている form with 失恋する implies that a person is getting their heart broken multiple times, and not that they are in an ongoing state of broken-heartedness.
失恋する is opposite to 振る. 失恋する literally means “lose love,” i.e. being rejected by someone whom he or she loves. While 振る means “to reject” a romantic proposal from someone who loves him or her. Its passive form is (彼女に) 振られる. “失恋する” and “振られる” are almost similar in meaning, with the latter having a stronger nuance of getting an outright elbow.