There are 3 main colors for white lights. They are namely:
1) Warm White - 2800K - 3000K
2) Cool White - 4000K - 4500K
3) Daylight - 6000K - 6500K
As it can be seen above, there is a range in the color of the light depending on manufacturer and what specifications they use. As a guide, below are the color differences. Warm being the most yellowish and daylight being the whitest.
These color are applicable for LED Lighting, Traditional Downlight, Bulbs and Lighting Tubes. In general, customers prefer to use warm light in sleeping room and living room to create a more cozy ambient. Cool and Daylight is a personal preference and they are generally used in Study rooms, Kitchen and Bathroom. Color choice of light is all about personal preference and there is no hard and fast rule.
There are also other considerations like when having elderly at home who may still have a preference for the daylight effect.
In modern lighting however, warm white is still the preferred for many as it creates a warmer, more cosy ambience.
Some feedback from customers and designers are that cool white may also tend to make certain furnishing appear "pale", while, daylight tends to create very defined shadows as a result of the color contrast.
That said, it also depends on the theme, placement and design elements when choosing the right ones for your home.
At the point of writing, we understand that cool white (4000K) LED lightings are not so readily available in the mass market (usually only made available through major lighting manufacturers), possibly because of the manufacturing cost which is a direct result of the lack of demand which is brought about by to the lack of education and availability in the market (generic manufacturers only choose to go for either Warm White or DayLight), although customers have been seeking a colour that sits perfectly between the most warm (yellow) and most bright (white) spectrum.
Hope this little article helps.