Yes, exactly, the meaning of 'safe string' depends on its context.

I personally believe that all code that is sensitive to escaping issues, should be escaped on output (or storage / sending to the database / whatever) by default unless you explicitly opt it out.

In our framework, we maintain 'already escaped' strings as a separate class, forcing the developer to acknowledge this fact. The HTML output layer escapes all strings unless they are instances of this safe class. Similarly for the SQL layer, all code gets quoted unless it was explicitly marked as 'safe'.