What is the difference between "This area is infested" and "This area is overrun by monsters"?
So, I was curious, and I've peek into the decompiled code.
It was found that there is no difference between this two messages. It just picks one at random to show:
Game1.showGlobalMessage(Game1.content.LoadString(random.NextDouble() < 0.5 ? "Strings\\Locations:Mines_Infested" : "Strings\\Locations:Mines_Overrun"));
I did a bit of searching and it seems that there's is no difference. Every site I come across says something like this : "If a level is "infested" or "overrun" by monsters, all enemies must be defeated on that floor before a ladder will appear" From the wiki, third line.
Another source: "For one, you may encounter a level that indicates it has been "infested" by monsters. On these levels you must kill every enemy in order to spawn the ladder." Guide to The Mines (Spoiler alert!)
It's just kill every monster and there seems to be 0 difference in "infested" or "overrun".