AMS-TeX is a TeX macro package, originally written by Michael Spivak for
the American Mathematical Society (AMS) during 1983-1985. It
is described in
``The Joy of TeX'' by Michael D. Spivak (second edition,
AMS, 1990, ISBN 0-821-82997-1). It is based on plain TeX, but
provides many
features for producing more professional-looking maths formulas with
less burden on authors. It pays attention to the finer details of
sizing and positioning that mathematical publishers care about. The
aspects covered include multi-line displayed equations, equation
numbering, ellipsis dots, matrices, double accents, multi-line
subscripts, syntax checking (faster processing on initial
error-checking TeX runs), and other things.
As LaTeX increased in popularity, authors asked to submit papers to the AMS in LaTeX, and so the AMS developed AMS-LaTeX, which is a collection of LaTeX packages and classes that offer authors most of the functionality of AMS-TeX.