I have added a screen recording as well.
In the first button, "Add Media" we ...

I have added a screen recording as well.
In the first button, "Add Media" we have margin-right to the button and we don't have any margin-left on the ajax-progress-icon.

In the second button, "Delete" we have margin-right on the delete button additionally we have margin-left on the ajax-progress icon. That extra margin-left is the issue.

Hope it is clear now.