Well, a quick Wikipedia check produced this nugget, which answers part of the question:
The use of closing credits in film to list complete production crew
and cast was not firmly established in American film until the 1970s.
Before this decade, most movies were released with no closing credits
at all. Films generally had opening credits only, which consisted of
just major cast and crew, although sometimes the names of the cast and
the characters they played would be shown at the end, as in The Wizard
of Oz, Mary Poppins, Oliver! and the 1964 Fail Safe. Two of the first
major films to contain extensive closing credits – but almost no
opening credits – were the blockbusters Around the World in 80 Days
(1956) and West Side Story (1961). West Side Story showed only the
title at the beginning of the film, and Around the World in 80 Days,
like many films today, had no opening credits at all.
And this came from a separate Wikipedia page, which answers the "Extra Credit" portion of the question:
The ascendancy of television movies after 1964 and the increasingly
short "shelf-life" of films in theaters has largely contributed to the
credits convention which came with television programs from the
beginning, of holding the vast majority of cast and crew information
for display at the end of the show.