• Was war er? (Nominativ question): ein gewöhnlicher Vogel
• Welcher Art war er? (Genitiv question): wunderbarer Art

Yes, you are right.

• Was war er? (Nominativ question): ein gewöhnlicher Vogel (adjective description of the bird)
• Welcher Art war er? (Genitiv question): wunderbarer Art (which species/kind (German: Art) does it derives from? => derivation is genitive casus)

Yes, you are right.