The title as written is accurate; what's confusing is other articles sometimes conflate these two things, and so some people also mix the two terms up.
Bananas fluoresce; squid bio-illuminate.
(I guess you think they are talking about the article but they explicitly said that they are talking about a story on the radio so I'm not sure where the confusion is coming from.)
That seems harsh. Couldn't it just be a fun general discussion of how light in nature among animals is observed?
Very, very different than bioluminescence. It is mildly interesting, but the comparison is really misleading.
Bioluminiscence.
I suspect in many cases it is simply the biologically cheapest 'sunblock'.
Also, the fur itself may degrade in UV, making it weaker, fading, and losing waterproofing and other properties the animal relies on.
And finally, the cost of fluorescence may be very small - meaning that it may have had some benefit at some point in the past, but there now no selective pressure to get rid of it.
This is used in a lot of biomedical imaging with infrared illumination yielding visible wavelengths.