What is meant if anybody talks about multibyte character sets?
That, as usual, depends on who is doing the talking!
Logically, it should include UTF-8, Shift-JIS, GB etc.: the variable-length encodings. UTF-16 would often not be considered in this group (even though it kind of is, what with the surrogates; and certainly it's multiple bytes when encoded into bytes via UTF-16LE/UTF-16BE).
But in Microsoftland the term would more typically be used to mean a variable-length default system codepage (for legacy non-Unicode applications, of which there are sadly still plenty). In this usage, UTF-8 and UTF-16LE/UTF-16BE cannot be included because the system codepage on Windows cannot be set to either of these encodings.
Indeed, in some cases “mbcs” is no more than a synonym for the system codepage, otherwise known (even more misleadingly) as “ANSI”. In this case a “multibyte” character set could actually be something as trivial as cp1252 Western European, which only uses one byte per character!
My advice: use “variable-length” when you mean that, and avoid the ambiguous term “multibyte”; when someone else uses it you'll need to ask for clarification, but typically someone with a Windows background will be talking about a legacy East Asian codepage like cp932 (Shift-JIS) and not a UTF.