It reminds me of recently getting lost in Phoenix mythology (outside the X-Verse).
The "Feng Huang" is the Chinese Phoenix, known for rainbow colors, narrow wings and a majestic long tail. In Japanese, it is "Ho-Oh". Hence the Pokemon.
In Chinese and Japanese lore, the Four Guardians are Byakko, Seiryu, Genbu, and Suzaku. Suzaku directly means "Red Sparrow", however, in a different context it can also mean "Red Phoenix". The direct meaning behind Moltres is Suzaku... but uses the connotation for Sparrow, despite the fiery imagery and the rebirth mechanic featured in the series. Complicated further by Talonflame, which directly translates as Red Sparrow as well in its kanji.
So to sum things up, the Feng Huang is not a Western Phoenix as we know it. Just like how Chinese dragons and Western dragons look so different. The X-Verse Phoenix is closer to a Suzaku, with the flame motif and larger wing set.