Wyrmwave is cast by Bahamut every time you use a spell that's on the GCD.
Everlasting Flight is cast by Phoenix when you use Firebird Trance(only at level 80).
Scarlet Flame is the same as Wyrmwave, but is from Phoenix.
Revelation is the same as Enkindle Bahamut but for Phoenix and will replace that on your bar when Phoenix is summoned