If the stealthy character is successfully hidden, in fact you can’t see them with normal vision—they’re too good at staying out of it. That’s the effect of blowing your perception check. The “invisibility”of being successfully hidden may be relatively easily broken by such mundane things as a change of vantage point without having to resort to magical means of cutting through an invisibility spell. But the basic equivalence of the condition is there as long as the failed perception applies.
IMO, there are two different physical states.
1. Invisible- a state (brought on by magic, or some other agent) in which someone, can stare right at you, and not see you. You cannot achieve
true "invisibility" with a Stealth check.
2. Unseen- That state by which you are literally "hiding in plain sight" but can be seen, if someone stares right at you, specifically looking for you.
These are brought on by a Stealth check all the time. Failed passive perception happens all the time, and many cat owners who have animals with
deceptive markings, like Brown Tabbys, can testify they walk by their cat all the time and simply don't "see" them, they go unnoticed, hence unseen.
They are in plain sight, perfectly visible, but the eye doesn't pick them out of the background, and discern they are there.
Yes there are ways to defeat invisibility, but if no one is looking for you, or notices, being unseen is just as good,
for many working purposes.
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