LaTeX is a program written in the programming language TeX. (In the same sense, any LaTeX document is also a program, which is designed to run 'alongside', or 'inside' LaTeX, whichever metaphor you prefer.)
Plain TeX is also a program written in the programming language TeX.
Both exist because writing your documents in 'raw' TeX would involve much reinventing of wheels for every document. They both serve as convenient aids to make document writing more pleasant: LaTeX is a far more extensive aid.
LaTeX is close to being a superset of Plain TeX. Many documents designed for Plain TeX will work with LaTeX with no more than minor modifications (though some will require substantial work).
Interpretation of any (La)TeX program involves some data-driven elements, and LaTeX has a wider range of such elements than does Plain TeX. As a result, the mapping from LaTeX to Plain TeX is far less clear than that in the other direction.