moon kinda a spin off from the earth. Something huge hit the earth, took a chunk off it, and this chunk or thing that hit is now the moon. May also have deposited iron during this interaction, which is now the molten core.
Generally it's believed that the sun and the planets formed at the same time from the same cloud of debris, gas and dust and that the lighter residue was mostly blown away when the sun ignited.
The larger debis continued to hit the early planets in the Hadean epoch the scars of which you can still see on the moon and mercury where ther's little atmosphere
No one proposed that the sun threw off matter which formed planets.
Our solar system is the second or the third hand debri of other stars. The heavy metals in this cloud of debri were apparently created during the final stages of other heavy stars and blown out when it exploded (supernovae).
When matter in this cloud got concentrated, the central part collapsed into the sun due to gravity, heavier elements (principal constituent of the rocky planets) were pulled towards the center and lighter elements (prime constituent of the jovian planets) remained outside. Subsequent collapses due to gravity and collisions reshaped the planets and their orbits in the solar system.
The moon was formed when a humoungous asteroid hit earth and tore a piece from it. We know this because rocks from the moon are same as the rocks from earth.
I do not profess to know the minor details but as an observer can't help believing the Earth and Sun were formed together from gases to give us our solar system and both were distinctly linked. This article suggests this: