Howdy akrapacs, and welcome to the forum!
Yep, cool on left, "neutral" on the right. However, don't think just because you have those two lights that you'll know what you're getting next time around when a dealer says "cool white LED" or "neutral tint LED". Every manufacturer has a different definition of those terms, and the only way you can know, at least some what, what you're going to receive, is to find the maker of the LED, then tint bin information. Even then, it's always kind of a waiting game for the light to arrive to actually see what kind of tint you're going to get.
Generally, cool white LEDs will be brighter (more efficient) than their warmer cousins. Some folks prefer the warm LEDs because they feel they give better color rendition, which is where we come to CRI, which is a whole topic itself, but helps to define an LEDs color rendering characteristics, but can only be taken along with the Kelvin color temperature to give an idea of what kind of light the LED will give off. One of my favorite LEDs is a Nichia 219, which has a CRI of 92 (closer to 100 is best) and color temperature of around 4500 (with 5000 being consider daylight). So, it's slightly warm, and renders colors very well.
Since most cool white LEDs, which tend to be more efficient (brighter), generally have a CRI of 65-75, they typically don't render colors as well....... so........... as flashlight aficionados, we have to make a choice. The brightest light possible, or one that renders colors better but is not as bright.
Some folks prefer the cool white LEDS for their clean white light, some prefer warm LEDs for their pleasing color rendition, and some are always on the quest for that elusive "NEUTRAL" LED, one that is neither warm, nor cool, but simply white, with no tint at any level. For many, the holy grail.
You're lucky, you've got both lights, so you can play with each one and see which one you like more. Some folks like cool lights inside and warm lights outside. Have fun deciding.
Derek