The 3800K and 4000K are not "ratings," but color temperatures. When you heat a piece of iron, it first glows a dull red, then yellow, and as it gets hotter it eventually turns a bright blue. A 3800 K lamp looks like the ideal laboratory standard "black body" heated to 3800 degrees Kelvin. For comparison, older sealed beam headlights were about 2500K and halogen lamps are about 2900K.
There are two ways to get the hotter 3800K and 4000K color temperatures. The lamps can be designed to operate hotter, but that shortens its life span. Physical constraints prohibit actually building and operating lamps at 3800 degrees, but PIAA and Silverstar may be hotter than other lamps which would give them a color shift in that direction. The other think is to filter out some of the longer wavelengths (reds and yellows) so the lamp looks hotter and whiter even though it is putting out less light.
A whiter lamp can look brighter physiologically even if it actually puts out less light (fewer lumens). A higher wattage lamp can start with more light, filter out some of it, end up with the same lumen output as a smaller lamp, and appear brighter because of the color shift.