Richard, Darwin did not originate the phrase "survival of the fittest" (that goes to Herbert Spencer), but he did use the phrase in The Variation of Animals and Plants under Domestication" (1868) and then in the 5th edition of On the Origin of Species.

https://en.wikipedia.org/wiki/Survival_of_the_fittest

However, you are correct the metaphor is frequently misinterpreted by the so-called Social Darwinists (mostly found in the field of economics and psychology and within the general public, not biology). Darwin was not pleased with how it was interpreted by the many.