A specialized set of textual formatting codes to apply to text.

You enter text into your wiki editing page. When you want to format that text (say, with italics), create a list or describe a table, you apply specific formatting codes. These are not HTML codes. Wiki formatting and HTML codes are not related to one another, except that wiki formatting was devised as a way to enter text quickly without having to memorize HTML codes or 'get them right'. This goes back to the days when most HTML formatting had to be entered 'by hand'.

Today, even many wiki mavens prefer WYSIWYG editing. Some, however, still swear by wiki formatting ... and at WYSIWYG editor. However, as onboard WYSIWYG editors approve, wiki formatting is likely to fade in importance.

Within reason, flexibility puts choices in your hands, rather than in the hands of your software vendor.

The main article about wikis includes this useful graphic:

Though HTML has suffered its share of politics and incompatibilities, it remains - relatively speaking - a highly standardized, common protocol. By contrast, wiki formatting standards tend to vary more widely from one wiki version to another. You cannot count on the same formatting codes working across different wiki products. Most likely, the opportunity for a single standard to emerge has already passed.