Webdings and Wingdings and other 256-character symbol fonts are not intended to work on the web. They do not work consistently on the web, unless you use them in something like a PDF file or some other file format in which the font is embedded. Only in such cases are they guaranteed to work.
Otherwise, in normal HTML, XML, and forum usage, ONLY Unicode characters in Unicode fonts are guaranteed to come out roughly the same on most browsers.
The old symbol fonts use a technology in which the symbols are understood by their order in the font, not by their Unicode values, because they don’t have Unicode values in those fonts. Don’t try to use Zapf Dingbats, Symbol, Wingdings, Webdings or any other symbol font on the web in HTML or XML or a post in a forum. You will often be disappointed. Old symbol fonts are those which are 256 characters, or less, in which the normal characters are replaced by odd symbols and pictures.
In Unicode, unless a font has an error in it, if two fonts have symbols in the same code point, they will always be variants of the same symbol, though often the style is somewhat different. That is why when a web site requests a font that you don't have and your system substitutes another font, it usually doesn’t matter much.
All the characters in the Symbol font are in Unicode except for the square root extension character, save that ™ only occurs once in a font as serif or sans-serif depending on the font.
Some of the Wingding characters are in Unicode, but with different encodings. See http://www.alanwood.net/demos/wingdings.html . This page, in the first column, indicates how they may be interpreted on Windows machines where Windows is set up for a Western European language such as English. Some browsers will display the Wingdings characters properly but many will not and by HTML and XML standards they are not supposed to.
You can use the Unicode hex method on the Macintosh to enter Unicode characters. See http://ipa4linguists.pbworks.com/Mac+IPA:+Main+page .
The first page I linked to also says, correctly:
“For Windows, browsers such as Google Chrome, Internet Explorer and Netscape 4 that are not standards-compliant allow non-Unicode fonts such as Wingdings to be specified in HTML or CSS, to enable additional special characters to be displayed. Specifying Wingdings font is contrary to the published specifications, has never been a documented feature of HTML, is not reliable, and should not be done. Wingdings is not available on all computers, and so the intended characters may not appear on computers running non-Microsoft operating systems such as Mac OS 9, Mac OS X 10 or Linux. The intended characters are also unlikely to appear when using a standards-compliant browser such as Firefox, Netscape 6+, Opera 6+, Safari 3+ or SeaMonkey (formerly Mozilla). The same problems are found with the Webdings, Wingdings 2 and Wingdings 3 fonts – they should not be used in Web pages.”
This applies to the Macintosh also.
See also http://www.skynet.ie/~caolan/wingdings/proposal/ , http://pagesfaq.blogspot.com/2008/03/how-do-i-type-wingdings-in-pages.html , and http://girtby.net/archives/2005/03/17/dont-use-wingdings/ .
For lists of all Unicode characters currently available, see http://www.unicode.org/charts/ , and http://en.wikipedia.org/wiki/List_of_Unicode_characters , and http://www-atm.physics.ox.ac.uk/user/iwi/charmap.html for those under U+010000 . Note that browsers other than Firefox have problems displaying some of them, even if you have them in a font.
For a Unicode symbol font, try the free Symbola font from http://users.teilar.gr/~g1951d/ .
Note, if you set your font in a word processor or an editor to Wingdings, then it will appear properly there, but still won’t paste properly into other applications unless the font Wingdings is also set there, and will still not paste properly onto the web in a format where it is universally visible.
Don’t use non-standard (non-Unicode) fonts if you can avoid them and don’t use them for characters on the web, except in something like a PDF file.