No, the wide characters (it's their name) are special code points. I guess it exists because someone wanted to be able to use one letter in place of a Japanese character while using the same width. The "normal" letters are called "half-width" here.
Full-width characters are relics from multiple legacy character sets. For example JIS X 0208, the primary Japanese two-byte character set, has a set of alphanumeric characters in the row 0x23, but their widths are not specified and it is totally possible to map them into half-width characters when no other character sets are in use. However it is most commonly paired with JIS X 0201 which is a single-byte character set with their own alphanumeric characters, so anything from JIS X 0201 is made half width and anything from JIS X 0208 is made full width to simplify implementations. This practice got stuck and subsequently followed by Unicode. Same for other languages.