Let me go through a few examples in my own life.
Mathematics is often near the top of my lists of interests. During high school, I was a silver medalist in the Australian Mathematics Olympiad and was probably in the top 10–20 in the country (although not good enough to make the team for the International Mathematics Olympiad). I only say this to justify that I at least had a shot of making a career in the field. At university, I started off majoring in mathematics and physics with an eye to being a theoretical physicist.
My choice of mathematics units (where I had a choice) strongly favored pure mathematics, but I think that was in part because "applied" mathematics in my course didn't mean things like theoretical physics but more things like dynamic programming and operations research. I much preferred topics like group theory over numerical methods.
But over the twenty years that followed, what I kept coming back to (and buying books on) was the mathematical foundation of general relativity and, to a lesser extent, quantum mechanics.
I'd read lots of books on differential geometry but I realized my interest waned dramatically if it wasn't relevant to understanding general relativity.
So really, my interest in mathematics can be far more precisely subsumed in saying my interest is in general relativity and cosmology.
That alone summarizes my shallow, broad interest in mathematics in general, my deeper interest in linear algebra, my even deeper interest in tensors, etc.
I could even get excited in numerical methods nowadays, if the application were computational relativity and cosmology.
This also summarizes my particular interests within physics and my deeper interest in astrophysics; why I'm interested in quantum physics but less so its practical aspects.
So rather than list 10–15 or so interests across mathematics and physics, I can probably just say cosmology and neatly cover everything.
Well, almost everything because there are still areas of mathematics that might be a necessary foundation for another interests outside of cosmology or physics all together.