Technically, they are quite similar. But they seem to have somewhat different purposes.
I believe a glossary should contain domain-specific terms that are not ambiguous but, rather, likely to be unknown to the reader. It should convey a general meaning of these terms.
A nomenclature, on the other hand, should show the reader how your particular document (formally) defines notations, terms and symbols that are ambiguous in general. This is particularly useful for scientific papers. Papers in mathematics or computer science, for example, depend heavily on exact definitions of e.g. the
+ operator or the letter
\gamma. They are also notorious for each having their own interpretation of otherwise generic terms like 'asymmetric' (math), 'strongly typed' (computer science) or 'kingdom' (politics, biology).
I'm not sure about all this (not being a linguist), but my intuition is based on the meaning of the words glossary (terms that are either newly introduced, uncommon, or specialized) and nomenclature (assigning of a word or phrase to a particular object, event, or property), as well as the kinds of features offered by these packages. For example, nomenclature packages often offer special support for mathematical symbols while glossary packages are more likely to offer multi-lingual support.