Character Set
A defined collection of characters and their numbering system. ASCII, ISO 8859, and Unicode are representative examples.
A character set is a defined collection of characters and the code points (numbers) assigned to each. ASCII defines 128 characters, ISO 8859-1 defines 256, and Unicode defines over 140,000.
Character sets and character encodings are different concepts. A character set defines "which number is assigned to which character," while an encoding defines "how that number is represented as bytes." Character encoding explained books provide systematic coverage.
HTML's <meta charset="UTF-8"> technically specifies character encoding, but the name "charset" (character set) is used for historical reasons.
For character counting, the character set determines the range of representable characters. ASCII cannot represent Japanese, while Unicode handles characters from around the world. Internationalization and character codes books provide additional context.