If you don't specifically link them to the plants in the database then they won't show up in their list. For example, the tag for that Onoclea sensibilis is actually the numeric plant ID of the plant itself. So the database finds the link and can print out the nice features including the full name and link to the plant in the "Plants tagged in this photo" area.
But the other tags just have words typed into them and that doesn't help the system make those connections between database entries and a particular tag.