A
snippet is PHP code whose output is displayed on the final web page. It is inserted into HTML code with [[...]] tags or [! ... !] tags. It basically replaces the <?php ... ?> tags in HTML.
A
plugin is PHP code that is inserted into the MODx core code at specified points during processing called "events". These can be events in the document parsing process, or during a login process, or just about any of the core processes. Some snippets include their own events, such as the eForm snippet for validating and emailing form posts. This way you can change the behavior of MODx itself without hacking the core code.
A
module is an addition to the Manager features. A commonly used module is the DocManager module, which provides more ways to manipulate the documents, particularly in bulk operations. Another module I always add to my sites is a full backup module that zips up all the MODx files along with a database dump, making the resulting zip file available for download/upload/extraction.
You may find this interesting
http://www.sottwell.com/modx-from-the-inside.html
The text in the AjaxSearch form is in the assets/snippets/ajaxSearch/lang/<your-language-file>. Most complex snippets will have a directory for language files that hold any text the snippet displays.