What about iso-8859-1? Is it encoding or character set or both?
Historically, it was described as a coded character set: it defined both a set of characters, and a mapping of those characters to byte values — what we would today call an encoding, but it was not explicitly described in those terms.
When Unicode was created, it was designed to encompass (nearly) all characters in widely-used character sets, and hence it recast the byte stream defined by the ISO-8859-1 coded character set as an encoding of the wider Universal Character Set.
So if you are working in a modern Unicode environment you would consider ISO-8859-1 to be an encoding. But it can't really be said to be wrong to consider it also a character set.
(There are other encodings which are definitely not character sets: for example the UTFs, and multibyte encodings like Shift-JIS, which was itself defined as an encoding for the JIS X 0208 character set prior to Unicode's extend-and-embrace.)