Whether it is a true bird or a creature of flames is undetermined. Both perhaps. Like Nature though, the phoenix never really dies. It's just stuck in an endless cycle of life and death.
As with the other level four summoning spells, this casts a fairly useful number of Phoenixes, though it is probably best cast after one or two rounds of casting buff spells such as Mass Fortune and Dragon Strength.
If you have a choice, which level 4 creature to summon is largely a question of personal preference and tactical situation.