Peanut does the clicky wing thing for the same reasons as people have listed... and would also when she's "in the mood" and wanted to mate with my hands.
It is the posture female birds take when waiting for the male to mount them, not to get too graphic or anything just so you're aware. I've heard female birds will sometimes hump, no idea if male birds do the female behavior outside of a same-set mated pair? Maybe someone with male lovies will know.
She's not nearly as hormonal as a senior so I almost never see mating behavior anymore but she still does the more violent version when she sees a particularly hated object like snow gloves or hears tape peelings sounds. Tape noises make her scarily angry for some reason.
There are some differences in her body language between the two, the expression in her eyes and is generally more "intense" seeming when upset with threatening beak grinding added to the clicking. When it's mating behavior she tends to be more clicky and spin in tiny circles; the worlds single worst lap dance.
I never was able to figure it out why other than potentially just a response to being over-excited/over-stimulated. One use is flirty, the other is aggressive/assertive.