The examples you are referring to are not examples of strings, but of patterns. A pattern may be delimited by any character (except alphanumeric characters), although the most usual one is
/. This does not seem to be very well documented, but I found it described under
:h E146, which reads as follows:
Instead of the '/' which surrounds the pattern and replacement string, you
can use any other single-byte character, but not an alphanumeric character,
'\', '"' or '|'. This is useful if you want to include a '/' in the search
pattern or replacement string. Example:
Strings, on the other hand, are either literal strings, e.g.
'this is a literal string', or "expression" strings, e.g.
"this is an expression string". See
:h expr-string and
:h literal-string. The difference is that the expression string accepts special characters that are parsed, e.g. special keys such as
"\<cr>", while literal strings are taken as is, except that double quotes are treated as a single quote.