Wet-bulb weather is when, because of a combination of humidity and heat, you can’t naturally cool off with things like sweat.

This isn't quite right, even though the gist of it ends up being right. This is one of very few things I'm legitimately an expert in, so I don't want to let it go uncorrected not because it makes a big difference, but because it just feels weird not to and maybe somebody will be interested.

Dry bulb temperature is what you typically read when you're looking at a thermometer. The bulb, the thing that's checking the temperature, is literally dry. To get a wet bulb reading, you essentially put a wet sock around a thermometer (to get a "psychrometer") and swing it around for a while, because you get a different reading when the water is evaporating off it. So when the air is fully saturated (100% humidity, standing in a cloud), your wet bulb and dry bulb readings will be the same. In all other cases, your wet bulb temperature will be lower.

"Wet bulb weather" isn't really a phrase people use. High wet bulb, high relative humidity, high absolute humidity - all the same thing (and in fact, if you have just one of those and the dry bulb temperature, you can calculate the others). They just measure how wet the air is in slightly different ways.