I agree that
Frodo's ability was enhanced, but I still think he didn't suddenly see Nenya, but suddenly understood what it was (for myself, I'm not sure I would have noticed
Galadriel was even wearing
a ring until she made her notable gesture under
Earendil). When Frodo saw Nenya, it's likened to a star,
"... as if the Even-star had come down to rest upon her hand. Frodo gazed with awe; for suddenly it seemed to him that he understood."
Tolkien has
Sam see a star too (for myself, I'm not suggesting Sam had his head in his hands the whole time, but to my mind he was still upset and distracted by his vision -- still referring to the
gaffer at the end of this scene), but even if Sam had realized the star was a ring, he couldn't perceive/know that it was one of the Three.
Galadriel says this to Frodo, and in the next breath turns to Sam.
"And did you not see and recognize the ring upon my finger? Did you see my ring?" she asked, turning again to Sam.
To me, the second part seems an abbreviated form of the same question to Frodo. And Sam doesn't say that he saw nothing, but that he saw the same "seeming image" that Frodo saw -- a star -- but he's not a ringbearer of course, and even after Galadriel asks her question, Sam's response still includes what I believe to be his main distraction through all this, his vision, including
"them digging up the gaffer and turning him adrift."
And Frodo's question to Galadriel (
the one he meant to ask
Gandalf in
Rivendell) reads:
"I am permitted to wear the One: why cannot I see all the others and know the thoughts of those that wear them?"
To me this is not merely about visual sight at a given meeting with someone, for example (not that anyone said otherwise), but goes to the very perception that
Sauron desired with his ring ruse: you put on the One, and you can "see" the bearers and their thoughts. But as noted (Galadriel says), Frodo has not tried this. Yet even so
"your sight has grown keener. You have perceived my thought more clearly than many that are accounted wise."
I would say sight/perception/recognition.
Elrond may have also worn
Vilya openly on his finger only in select times, but on the other
hand (cough, pun intended), generally speaking, Elrond wearing jewelry doesn't necessarily mean he's wearing Vilya.