First things first...as it was ORIGINALLY written, there WAS NO COSMIC FORCE CALLED THE PHOENIX FORCE. The events of the shuttle incident, meaning Jean desperately committed to saving her fellow X-Men, pushing her powers to the limit to survive the most intense solar flare on record, caused a breakdown of the mental blocks placed in Jean's mind by Xavier(which at first blocked off her telepathy completely, and limited her power in general), which in turned caused Jean to realize her full potential as a psi...she briefly became a being of pure thought, before refomring as Phoenix.
Later on, after the M'kraan crystal incident(where she first tapped in to the true nature of her powers), she instinctively erected her own mental barriers, to cut her powers back down from their cosmic peak...she was still extremely powerful, but this allowed her powers to be within her control. Eventually, through the manipulations of Emma Frost and Mastermind, they began tapping into primal dark emotions within Jean. While in their control, as The Black Queen, Cyclops used his psychic rapport with Jean(which was established earlier), to enter Jean's mind...he found Mastermind in there and they dueled. Scott "died", and the shock of seeing this snapped Jean back to her senses and broke mastermind's hold on her and she helped the X-Men defeat the hellfire club...this also broke through the mental barriers she had placed in her own mind, and combined with the dark emotions that had been stirred up by mastermind, she became Dark Phoenix.
All references to "cosmic force/entity" "cosmic clone" etc, came from the 1986 retcon, and NOT the original story...so it is not a contradiction of the original story for Jean to be Phoenix...that's how it originally was. Even after the retcon, it was still stated that Phoenix represents Jean's ultimate potential. It has now been re-established in the comics(Claremont's stories, Morrison's New X-Men, Endsong, etc) that Jean=Phoenix.
Anywho...yes I liked X3's explanation, despite it being rushed(like the movie in general).
X1...Jean is first affected by the residual radiation from Magneto's machine...in essence, this replaces the solar radiation from the shuttle incident in the comics. Remember that Xavier said "there appears to be none" referring to effects on mutants...this is an ASSUMPTION, not a fact, and for the most part it's true. Why is Jean different? Because of the nature of her powers...her powers are mental. Magnetism and telepathy have a relationship in the comics(brain waves, electric impulses, etc). Magneto has used his powers several times to block psychic probes, and has even projected an astral image of himself back in the wacky pseudo-science days of the 60s. We clearly see a reaction from Jean after the machine shuts down...it was talked about on the commentary track, and it was later referenced to specifically by Cyclops in X2...this was the start of the mental block breakdown.
X2...her powers are expanding, or rather, she's able to access more of it(semantics really). There are control issues, likely related to not being used to this increasing scope of her powers. Also, since the blocks are only weakened, not completely dissolved, she essentially has "power outtages"(her power shutting off after destroying the first missle for instance) or other side effects(affecting electrical equipment around her, which is my take on why she left the plane...greatly supported by a deleted scene of her manipulating the plane controls telekinetically while en route to Nightcrawler, and causing electrical interference). Near the end of X2, when Cyclops shoots at her, she's forced to draw on more power to protect herself, which, due to the blocks still being there, causes an unstable burst of power, knocking both Cyclops and herself back and causing collateral damage to the dam. At the end, she commits herself to saving her friends. She is still unstable, but she's 100% committed and there's no room for error...she seals up the jet, powers it up, prevents nightcrawler from teleporting to her, blocks the water, lifts the Jet, and says her goodbyes via Xavier. This is very similar to the shuttle incident where she commits herself, prevents Cyclops from talking her out of it(she telepathically forces him asleep), and pushes herself to her (perceived) limit to save them.
X3...she "dies", but her subsconscious mind protects her via her telekinetic powers. In the comics, she essentially appears to herself in gold-woman form, an aspect of Jean's personality called Phoenix, who says she can save her by merging with her, creating a new body, and putting her radiation-ravaged body in a healing cocoon.
When Jean returns, her powers are fully unleashed, and so is the other side of her personality. Now the problem with the movie is that there is little time for development, so it's mostly "evil" Jean we see, with little transition to "good" Jean save for the med lab scene. Since everything is crammed into one movie, and worst, is shared with the cure plot, there's no slow build it, so it just seems like Jean's problem is with power, when that really wasn't the case. She handled power just fine in the comics, it was the stirring up of her inner dark emotions that made her lash out and be wreckless with her powers.
Anywho, for all intents and purposes, Jean in X2 was the movie version of "Phoenix" and Jean in X3 was the movie version of "Dark Phoenix". X2 Jean had the same growth in power yet instinctual inner barriers and power inconsistencies that comic Phoenix had, and in X3, Jean's powers were at their max and her personality was malicious, just as they were when she was Dark Phoenix(creating a wormhole in space, devouring a star, etc).
