In the interior lighting world, 2700K-3500K is "soft white", warmer is "warm white", ~4000K-4100K is "cool white", and 5000K+ is "daylight". This dates back to the CFL days, and is still used for the LED bulbs. Also 8000K-12000K for car headlights was called "blue" ;)

Around here, warm white is usually anything below 4000K. Neutral white is disupted territory, but usually 4000K-5000K (And typically not much cooler than 5000K at all). Cooler than that is cool white.