In several questions and answers on this site I've read phrases that suggest there can be a scale of synonymity between words—something I haven't thought much about before. Some examples I've seen are almost synonymous, nearly synonymous, somewhat synonymous, almost completely synonymous, and absolutely synonymous. I'm wondering if there's a more formal and accurate way to classify these apparent degrees of synonymity. I did find one highly specialized online article on this subject, but it made my head hurt. So I guess I'm also wondering if there's a CliffsNotes version for the layperson.
The question can be answered with semantic concepts.
The degree of synonymy can be describe as total or partial synonymy. For this you have to consider the term as a lexical unit - a lexeme, which is basically the lexical entry including grammatical category, grammatical forms and properties as well as its lexical meanings. Here we find with the most terms what is called polysemy, i.e. the meaning variants a term can take without being a different lexem (that would be homonymy). If you look up the adjective "smart" you will find that in some menaing variants the synonym can be "clever" or "intelligent" but not in all contexts "smart" can refer to, thus not in all its meaning variants. Another example for partial synonymy would be "America" and "USA" which can in the right context both refer to the United States, but in others "America" is a broader term referring to the whole geographical continent. Total
However, the synonymy expressed by "almost" or "nearly" might be intuitively, that some terms add a slightly different aspect to the meaning than the (lexical) synonym.