Yes the terminology used by light manufacturers is for their own marketing purposes.
The light strips in the "natural to cool" range of 6000k or so will bring out your animals colors nicely.
The newer light strips on the market will put out the light needed for display purposes, so long as you use one that has the output/density for your needs.
These cages are four ft long and two ft high using a single wide high output 36" strip light. It lights up these cages like high noon!
Super Bright LED has a nice selection of strip light tapes.
High Power LED Flexible Light Strip - NFLS-X3 | Top Emitting | Flexible LED Light Strips | LED Light Strips & Bars | Super Bright LEDs
This is what is used in the cage above, the "natural white" is 5600k, but it has the output to light a large cage with a single row of tape. Very cost effective.