There's a similar concept for plugins called shortcodes (as andrewk said). The syntax for these is slightly different than the more tag (which does look a lot like an html comment). Shortcodes are wrapped in square braces like so:
[myshortcode arg1="something" arg2="something else"]
Shortocde is the term for the technique, but plugins that implement shortcodes don't have any special name or anything. They're just plugins that use the shortcodes API. Similarly, plugins that use the widget API (or any other WP functionality) don't have special names. They're all just plugins.
As far as I know, there is no built-in API for implementing "html comment-style" tags like the more tag. And I don't think the technique is in popular use by plugin developers since the shortcode API became available. At least, I don't see it very often.