What is the difference between modulo and modulus? Throughout my education in computer science, I feel like I've heard the terms "modulo" and "modulus" used interchangeably.  It looks like even Wikipedia claims that "modulo" is "sometimes called 'modulus'" (see the first sentence of the page on 'modulo').

I've looked into this issue a little and it seems that "modulo" finds singular use in modular arithmetic (e.g. "19 and 64 are congruent modulo 5").  In addition, I've seen the symbol % be referred to as "modulo."

Meanwhile, "modulus" appears to have several definitions, including "absolute value" and "constant factor" as well as referring to the "5" in "modulo 5."

Is it ever correct to use these terms interchangeably in the context of computer science?  Are they simply different types of words that represent the same idea (such as "run" and "runner")?  Are there important differences in other disciplines?

Bonus: Etymologically, what gave rise to these two terms?
"modulo" is an operator.  For instance, we might say "19 and 64 are congruent modulo 5".

"modulus" is a noun.  It describes the 5 in "modulo 5".  We might say "the modulus is 5".

No, the two should not be used interchangeably.  It would be incorrect to say "19 and 64 are congruent modulus 5".  It would also be incorrect to "the modulo is 5".

See also https://en.wikipedia.org/wiki/Modular_arithmetic and https://en.wikipedia.org/wiki/Modulo_operation.  Both define the word "modulus", and as far as I can see they use it correctly.