For section names, no. There's nothing special about the title of the "See also" section versus any other section on any other page, unless the wiki is specifically loading i18n messages for section headings like Commons does.

For interface messages, you'd need to determine the message key. Then you can query them from the API (action=query&meta=allmessages) or you can look on the wiki in the MediaWiki namespace. For example, the text of the "edit" tab in the Vector skin comes from the message 'vector-view-edit', so if you want to see what that is in German on your wiki you could check MediaWiki:vector-view-edit/de[1] or api.php?action=query&meta=allmessages&ammessages=vector-view-edit&amlang=de.[2]

 [1]: https://en.wikipedia.org/wiki/MediaWiki:Vector-view-edit/de
 [2]: https://en.wikipedia.org/w/api.php?action=query&meta=allmessages&ammessages=vector-view-edit&amlang=de