Often confused to have been astral projections or transformed Sephiroth Clones being controlled, the majority of the Sephiroth forms seen throughout the game are pieces of JENOVA -- as well as JENOVA's entire body -- in Sephiroth's form. We know that JENOVA's pieces took on Sephiroth's form for the following reasons: JENOVA's Cells can change their form ("Sephiroth: 'Cloud... Don't blame Tifa. The ability to change one's looks, voice, and words, is the power of Jenova.'"), so it would be simple enough for its pieces to appear as Sephiroth. When the forms of Sephiroth fly off into the air those times they're encountered on the Shin-Ra cargo ship and in the City of the Ancients, boss battles against parts of JENOVA follow, and in the case of the form flying away at the City of the Ancients, something falls, it being a piece of JENOVA. Many have taken this to mean that Sephiroth, a Sephiroth Clone with an altered appearance, or an astral projection of Sephiroth capable of physical interaction flew away and dropped the pieces, due mainly to Cloud's statement on the cargo ship that Sephiroth was carrying JENOVA ("He was carrying Jenova with him"). However, no rendering of Sephiroth carrying anything at that point was placed into the game, even while JENOVA's head was rendered during the scene in which Sephiroth carries it. The validity of Cloud's statement can further be called into question as, perhaps, having been an assumption on his part; AVALANCHE had just been knocked to the floor -- as they would be later in the Whirlwind Maze -- as the Sephiroth form flew away, and possibly wouldn't have had a good look at the Sephiroth form as it ascended into the air in the first place, so with a piece of JENOVA falling and transforming before them, he may have simply assumed Sephiroth must have been carrying JENOVA's body.
Despite Cloud's statement, there is evidence that bosses were actually the Sephiroth forms themselves, transforming to face the party. First, in regard to the real Sephiroth having been present, his real body had been encased in Mako in the Northern Crater all this time, and could not have been off doing those things seen in the game. Further, of his own body, only the torso remained. In regard to the possibility of transformations, when Aerith is murdered, the Sephiroth form that killed her rises into the air and vanishes in a flash of light, followed by something falling to the ground from the spot where the Sephiroth form had been, commencing the battle against JENOVA-LIFE. At the end of the battle against the creature, JENOVA-LIFE finishes the sentence that was previously being spoken by the Sephiroth form:
Cloud
"My fingers are tingling.
My mouth is dry.
My eyes are burning!"
Sephiroth
"What are you saying? Are you trying to tell me you have feelings too?"
Cloud
"Of course! Who do you think I am!?"
Sephiroth
"Ha, ha, ha...... Stop acting as if you were sad."
"There's no need to act as though you're angry either."
Sephiroth
"Because, Cloud. You are..."
::The battle with JENOVA-LIFE commences; when the battle ends, the screen fades to black::
Jenova
"Because, you are...... a puppet."
Also consider that the Sephiroth form seen at the Northern Crater -- who slaughters the Sephiroth Clones that had been Hojo's experiements from Nibelheim -- descends upon the party, lands near them, turns to face them in a battle ready position, just as AVALANCHE stands and prepares to fight, and before the battle against this being begins, the form of Sephiroth is seen on the environment map as being AVALANCHE's opponent, yet when the battle begins and switches to the battle map, JENOVA-DEATH is in the Sephiroth form's place. The scene further shows that Cloud had realized that it had not been Sephiroth that AVALANCHE had been chasing at all:
Cloud
"Sephiroth!!!"
::AVALANCHE runs toward Sephiroth and stands behind him; he doesn't turn to face them::
"This is the end!"
Sephiroth
"You're right. This is the end of this body's usefulness."
::The area goes dark and Sephiroth vanishes, leaving only a plume of dark smoke::
Cloud
"He disappeared!?"
Tifa
"He might still be nearby......"
...
::Later, Sephiroth reappears, hovering above the party as the light returns to the area, with his sword drawn. He descends upon AVALANCHE, knocking them to ground as he had done back on the Shin-Ra cargo ship. He then lands and slowly turns to face them and assumes a battle ready position as AVALANCHE gets back to its feet; the battle with JENOVA-DEATH commences::
Cloud
"Jenova's cells..."
"...hmm. So that's what this is all about."
"The Jenova Reunion..."
Tifa
"Not Sephiroth!? You mean all this time it wasn't Sephiroth we were after?"
::Cloud shakes his head::
This scene also shows that -- with the Reunion complete by killing Hojo's experiments and some falling down into the Northern Crater where their Cells could be reclaimed -- that piece of JENOVA would have no longer needed to go about in Sephiroth's form, thus, the line "This is the end of this body's usefulness."
Also notable is that when JENOVA-DEATH is defeated, left behind in its place is the Black Materia, which Cloud had handed over to a Sephiroth form earlier in the game.
At this point, one could argue that this only proves that the Sephiroth forms are what transformed into the JENOVA bosses, and not that they are pieces of JENOVA. However, referring back to JENOVA-BIRTH, when it is defeated, it reverts into a tentacle of JENOVA that the party recognizes as having been part of JENOVA's body back in the Shin-Ra headquarters:
Tifa
"I've seen this somewhere... before."
Cloud
"...Jenova. The arm of Jenova."
Aerith
"Jenova... With this thing?"
Just for clarification, it should be noted that the Sephiroth form on the Shin-Ra cargo ship was more than likely the entirety of JENOVA's body which had escaped from the Shin-Ra headquarters. In the instances of the slaughter of Shin-Ra personnel in both cases, either Red XIII or a Shin-Ra employee makes note that the perpetrator isn't human, and back in the Shin-Ra headquarters, JENOVA's containment vessel appeared to have been blasted open from within. Further, Palmer makes no note of the Sephiroth form that killed President Shinra carrying JENOVA with it. This is because it was JENOVA. Also notable is that the Sephiroth form on the cargo ship doesn't recognize Cloud, whereas later forms of Sephiroth that show up do.
With all this in mind, the Sephiroth forms encountered throughout the game were most certainly pieces of JENOVA -- or its entire body -- in Sephiroth's form, the exceptions to this, of course, being those seen after JENOVA-DEATH was defeated. Both of the Sephiroth forms seen after that point were astral projections. It should be noted that neither of these performed any kind of physical interaction (the picture that the one inside the Crater lifted was also an illusion), and both vanished, though not in the same manner as did the one in the City of the Ancients, which emitted red light with JENOVA-LIFE falling from its position.