In TiddlyWiki parlance, a server side is a web-based service that provides storage of TiddlyWiki data on a web server so that it can be accessed from multiple client machines and potentially multiple users.
There are several different server sides for TiddlyWiki. Some store entire TiddlyWikis as the addressable unit, others store tiddlers as the addressable unit.
TiddlyWeb is the latter type to such an extent that it has now become common to use TiddlyWeb to manage and host applications that work with tiddlers without ever using TiddlyWiki.