stem or root?

Besides their more special meanings, the words "stem" and "root" are both
used to denote the core part of a word to which affixes are attached. Are
the two words synonymous in this context?

In the German language, there are many words that look as if they had an
affix (mostly a suffix) but this affix appears in each cognate word, e.g.
"Wagen" with the suffix "-en", but all not to distant cognates contain the
n of the suffix, e.g. "Wagner". The "-(e)n" thus belongs to the word
itself and is not an *additional* affix. Would one say that it is part of
the root? Or that it is part of the word stem?

Without being sure about the correct terminology, I would consider it part
of the root but not part of the stem, but I want to check whether my
terminology is correct in this point.

--
Helmut Richter
.