You cannot "improve" the tag wiki because you don't have full editing privileges for tag wikis yet. That requires "trusted user" status, or at least 20k reputation.
Until you become a "trusted user", you have to suggest edits to tag wikis and have them approved by other community members just like the person who suggested the initial edit.
Approval/rejection of tag wiki edits is a significantly lower bar, only requiring 5k reputation.
The reason that you can use the "Improve" button on edits to regular posts is because you do have full editing privileges for regular posts. Anyone over 2k reputation has that privilege, the same group of people who can accept/reject suggested edits.
There used to be a bug where the "Improve" button was shown for users without full editing privileges for tag wikis, but clicking on it lead to an error page. The UI has since been improved so that the button is not shown at all when it does not apply.