It's called brevity Young.
Brevity wins out over precision most days.
Jean Grey Dark/Phoenix in the 70s was a fake. An Avatar. The real one was asleep under Hudson Bay.
What about Rachel from Excalibur in the 90s?
If she was an Avatar that means that the "real" Rachel Summers is in stasis some where in an alternate time line having never played out any of the adventures we saw her in...
The First line to the wikipedia entry
The Phoenix Force is an entity in the Marvel Comics fictional universe which has bonded with other characters, who often used the alias Phoenix.
Did you ever read the issues of Quasar from around that time of the infinity gauntlet where Quasar was shown that the posers that control the universe have "abstract constructs" which we perceive we physical beings, becuase they are physical beings who 'Take care of business.
Hope is a bucket soaking up the dribble over from the Phoenix entity pissing suns worth of Phoenix Force in every direction.