In the UK, the common distinction is salted vs unsalted butter.

You want room-temperature butter so it's spreadable. Ripped bread and dry toast are awful, and nobody says "I'll take one portion of butter out of the fridge so I can have toast in 30 minutes from now".

Salted butter will survive being left at room temperature longer than unsalted butter, because the salt helps inhibit bacterial growth. Once you've thrown away your third half-eaten pack of unsalted butter because it's gone rancid before you could finish it, you get the picture.

Even in the fridge, salted butter lives longer than unsalted. So why ever buy unsalted? Because in baking, salt kills your yeast. Even if yeast isn't involved, you usually don't want salty cakes, muffins, pastry, etc.

Hence unsalted butter in the fridge for baking while salted butter for eating on the counter-top.

There's a WSJ piece on this topic in today's edition. Experts say it's generally OK to leave butter out on the counter for three weeks.

Who takes three weeks to go through a stick of butter???

Depends squarely on the country.

Where I am from they butter every visible piece of bread but you will be hard pressed to find a single household where butter is not kept in the fridge. In fact, I'd argue that the only country that keeps butter at the room temp seems to be the UK.

In the tropics, both butters go in the fridge. Heck, in the tropics, almost everything that's not a dry, dessicated powder or otherwise dehydrated goes in the fridge.

Where I live, 10 months of the year it makes no difference because it's going to be rock-hard and able to bend your knife no matter where you keep it. The remaining two months of the year butter left on the counter is a glorious yellow puddle.