"Survival of the fittest" is indeed not Darwin's term. It comes from Herbert Spencer, who had written a number of evolution-like pieces in the decade before the publication of the first edition of Darwin's Origin of Species (1859). The idea of a "struggle for existence" was very much "in the air" and both men were influenced by Malthus. Spencer went on to write any number of works that purported to be based on evolution, and he was at one point wildly influential.

In later editions of the "Origin," Darwin specifically said that his principle of descent with modification by means of natural selection could accurately be described by the term "survival of the fittest", and gave Spencer credit for the term.

RAS