Some people prefer not to commingle the functional, lambda-calculus part of a language with the parts that do side effects. It seems they believe in the separation of Church and state. --Guy Steele
A good paper describing functional programming and also talks about the differences between these two mindsets is "Conception, Evolution, and Application of Functional Programming Languages" by Paul Hudak (1989). You can find a copy at https://courses.cs.washington.edu/courses/cse583/00wi/p359-h....
I've talked with people who also see these two sides but call them differently.
As I see it, this book is closer to the algebraists side. Thus, you probably lean closer to the nuemerical side.
I also like to think about it as the Turing perspective (numerical, algorithmic) and the Chruch outlook, which is more algebraic-symbolic.
At the end of the day, it's both "contrasting" viewpoints coming together that truly animates the science of computing.