Responding as the person pemerton quoted, let me put it this way.
I believe that when the designers wrote "find you" in the last paragraph, they no doubt were thinking primarily of the Perception check mentioned earlier. Because, as I've mentioned elsewhere, they were assuming that any Hiding character would be trying to stay hidden, and therefore would require a Perception check. They no doubt assumed that any character coming out in the open from their hiding spot would be no longer attempting to hide. And sure, it's my speculation, but I'm 1000% certain they did not expect people to seriously entertain the notion that a character's successful attempt to hide behind cover or concealment would confer on them literal invisibility that would allow them to walk right up in plain view of some guards. They wanted to streamline the rules, so they removed such extraneous verbiage as "You lose the benefits of hiding when you stop hiding."
That said, the rule was not written so that "find you" is exclusive to a Perception check. The first paragraph is simply describing how a DC for a Perception check is determined. The second paragraph doesn't say, "...find you with a Wisdom (Perception) check." It doesn't say, "...find you as explained above." It doesn't say, "if the enemy's Wisdom (Perception) check exceeds your Stealth check". It just says "find you," and leaves the interpretation to the DM.
If a DM wants to interpret that "find you" as referring only to a Perception check (and therefore, in combat, only to a Search action, as Treantmonk inferred), and then get angry when that ruling forces them to let successfully Hiding PCs walk right up to guards, that's their prerogative. But RAW, "find you" includes but is not limited to a successful Perception check. So I know how I'll be ruling.
But why, Iosue? one might ask. Why would WotC write a rule that leaves so much to interpretation? Because, like many things in D&D, the quality of stealth will vary from table to table, from genre to genre. They want to allow situations where Hiding characters can run from one hiding spot to another without being seen. They want to allow Stealthy PCs to Hide in unique and fun ways (e.g., hiding in a crowd of people). Heck, some may even want to let characters take advantage of the guards looking another way to move straight from their hiding spot to right in front the guard, a la the docks scene in Batman Begins.
Not every table will want to do this. Some may want to make stealth super "realistic" (for certain definitions of realism), and so may interpret the rules more strictly. So, Hiding gives you the Invisible condition (which only gives you advantage on Initiative and attacks, makes you unaffected by anything that requires the enemy to see you, and gives enemies Disadvantage on attacks against you; it mentions nothing about being transparent), and this only ends when you make some noise, make an attack, cast a Verbal spell, or an enemy finds you. And that's all. How that works on the ground will be up to the DM.