Usually the two terms are synonymous, but it can get very confusing. I blew out a job interview many years ago by asking this very question of the Technical Director, and he didn’t know. I wasn’t trying to be awkward, I was genuinely looking for enlightenment, and given that he was asking me about loop stability margins I thought he might know.
The best explanation I’ve heard so far is that resonant frequencies are a subset of natural frequencies. If you like, a system may have several natural frequencies, and the ones with the strongest response are known as resonant frequencies.
Knowing the undamped natural frequency can be useful in some systems, and adding damping will lower the actual resonant frequency.