The bill of adult Trumpeter Swan differs from that of adult Tundra Swan in at least 3 traits, all of which can be hard to assess, even with photographs:
1. The shape of the line from the eye to the throat is flatter in Trumpeter. This line is caused by the lower edge of the bill.
2. The shape of the line across the top of the bill ("V" shaped in Trumpeter; "U" shaped in Tundra).
3. The thickness of the bill where it meets the eye (thicker then the eye in Trumpeter; thinner in Tundra).
These traits don't hold up for immature birds