Language codes for simplified Chinese and traditional Chinese?

There is indeed a standard representation for this. As people have run into the exact same problem you are seeing -- same language, but different dialects or characters -- they've extended the two-letter language code with a two-letter region code. So you might have a universal French page at mydomain.com/fr, but internationalizing for French Canadian readers might leave you with a mydomain.com/fr_CA (Canada) and mydomain.com/fr_FR (France). Some platforms use a dash instead of an underscore to separate the language and region codes (hence fr-CA and fr-FR).

The standard locale for simplified Chinese is zh_CN. The standard locale for traditional Chinese is zh_TW.

I hesitate to point you towards the actual BCP 47 standards documents, as they're, uh, a little heavy on the detail and a little light on the readability. Just go with standard locale identifiers, like the ones in used by Java, and you'll be fine.

Language is dependent upon where it is spoken (doh!), so language and locale codes reflect that reality. zh is the basic language code, but because there are two major forms of it, there are zh_Hans and zh_Hant, but they are still only language codes, not locales.

Location-specific

To fully specify which language is used in a particular location, the country code still has to be suffixed, so making zh_Hans_HK and zh_Hant_HK for simplified and traditional Chinese, respectively, both as spoken in Hong Kong.

Actually, the reality is that something more specific than country code is often required in many countries, but that is likely to exponentially increase the complexity and maintenance of databases like CLDR, plus the support infrastructure to feed into it, like IP to location details extraction, is not generally available or accurate enough.

Fixed text

Now, if the code is just to specify which set of fixed strings to use in the user interface, or even whole pages sets on a site, a country suffix is not really necessary, unless there are more than a few places where the language varies significantly enough (location-based info) to bother creating a whole separate resource set.

The larger the resource set, the more likely that a language code based upon locale [in this context, just a language attribute, rather than a true locale, so you can call it what you like!] will be required, but at least you only have to do that when necessary.

On-the-fly values

However, if wanting to format particular variable values, like dates, times, currencies and numbers, on-the-fly, locales become important, because all the tools that support such functionality (like those based upon Unicode CLDR data) expect them. The locale for these needs to be a separate setting to the code for which an in-house-generated UI language is set to use, unless you want to create a resource set for every known locale, and maintain them ad nauseum!

Browser language tools

Note that when specifying locale for a web page that can be edited, as in input boxes, and spellcheck in attributes or css has been enabled for the field, the browser's language tools will spellcheck the field according to that locale.

Criteria

You have to be clear about what the resource set is providing, so consider:

• Fixed strings? Language only.
• Formatting on-the-fly? Locale.
• Spellchecking in the viewing environment? Locale.
• Whole pages/subsite? Language only, else locale (as a language variant) if significantly different content required.

Spreadsheet to minimise maintenance overhead

I use a spreadsheet to hold UI strings where each language code has a parent code, so that the cell for its version of a string has a formula that gets its string from the parent. To create a custom string for that language and string, I just overwrite the cell formula with the exact text. That minimises the amount of resource maintenance. I run a macro at the end that generates a complete resource file for each language.

@dkarp gives an excellent general answer. I will add some additional specifics regarding Chinese:

There are several countries where Chinese is the main written language. The major difference between them is whether they use simplified or traditional characters, but there are also minor regional differences (in vocabulary, etc). The standard way to distinguish these would be with a country code, e.g. zh_CN for mainland China, zh_SG for Singapore, zh_TW for Taiwan, or zh_HK for Hong Kong.

Mainland China and Singapore both use simplified characters, and the others use traditional characters. Since China and Taiwan are the two with the biggest populations, just zh_CN and zh_TW are often used to distinguish the simplified and traditional character versions of a website.

More technically correct but not commonly used in practice, however, would be to use zh_HANS for (generic) simplified Chinese characters, and zh_HANT for traditional Chinese characters, except for rare cases when it is meaningful to distinguish different countries.

I'm just going to leave this here.