to so-and-so; he ascribed it to Abū Hurayrah; he ascribed it to Ibn ʿAbbās; he ascribed it to Ibn ʿUmar, and so forth.
Does providing an isnād automatically mean that the ḥadith is authentic?
We say: no, because the chain may run uninterrupted from the narrator all the way to the Prophet ﷺ, yet still contain weak or unknown transmitters and the like.
Accordingly, not every musnad is sound. A ḥadith may be ṣaḥīḥ while not being a musnad, as when it is attributed to a Companion with a reliable chain: the report is mawqūf and authentic, but it is not a musnad because it is not marfūʿ to the Prophet ﷺ. Conversely, a report may be a musnad with a continuous isnād, yet its narrators are weak; in that case it is indeed a musnad, but it is not authentic.
There is, then, a difference between the musnad in its linguistic sense and the musnad in its technical sense, the relation between them being one of generality and particularity.
Linguistically, a musnad is whatever is attributed to its speaker, whether it is marfūʿ, mawqūf, or maqṭūʿ. Thus, if you say, “So-and-so said such-and-such,” that is a musnad—even if you are referring to someone who is present and whom you are addressing right now. Likewise, if I say, “So-and-so said such-and-such,” that too is a musnad, for I have ascribed the report to its speaker.
Technically, however, a musnad is a marfūʿ report whose chain of transmission is uninterrupted.
Therefore, the musnad in technical usage is narrower than the musnad in linguistic usage: every musnad in the technical sense is a musnad in the linguistic sense, but not every linguistic musnad qualifies in the technical sense; hence the relationship is one of inclusion and exclusion.