Would you please assess the definitions below for me to see if I have correctly understood the concepts?
Seme: Semes are the smallest units of meaning of a morpheme.
Morpheme: A morpheme is the smallest morphological unit of meaning of a word.
Thus, the difference resides in a morpheme being a sign, while a seme is its associated meaning. E.g. in the lexeme "tree", we recognize one morpheme, signifying, depending on the level of analysis, multiple semes. Thank you!
Your comment in which you describe your understanding of the matter is correct, IMO, just the definitions would need improvement. Your definition of "morpheme" is hard to understand and far removed from standard definitions. But yes, basically, the morpheme is a unit that has a meaning, and the seme is a unit of meaning.
However, the usage of the term "morpheme" is fairly chaotic (IMO). For some people, a morpheme must be a real unit, a visible sign, similar to what is called a morph. But sometimes you find a notion of "abstract morpheme" which starts looking similar to a unit of meaning, and I think that's how your question came about. For example, it would sometimes be said that the word form "went" contains the two morphemes GO and PAST. I think in this case, the talk of morphemes is motivated by the idea that it is still something that should be a sign of its own, it just doesn't always appear as that at the linguistic surface.
That would amount to saying that morphemes are discovered by a procedure that looks at grammatical structures, and semes are discovered purely by comparing and decomposing meanings.
