curid is an url parameter to index.php. wgArticleId is a JavaScript variable present in the source code. Both refer to the page_id property of the page in the database.
They should be renamed to pageid/pageId, for clarity (especially wrt curid) and consistency (to match page_id in the database and the pageids API parameter).
To complete the set, a magic word would be nice, such as {{PAGEID}}, as simply a wrapper around wgPageId.
ps - I suppose old names could be kept as aliases for backwards-compatibility.
Version: unspecified
Severity: enhancement