No that's Cetra.
It doesn't matter about any similarities you come up with. The fact remains that the mechanics behind the use of magics in both worlds are different. In FF7 the thoughts of the ancients remain in the lifestream after they die and when the lifestream solidifies into materia regular people can use certain magic while in possession of certain materia. However in FF8 initially only sorceresses could use magic (and sorceresses are decended from the Great Hyne). Then Dr. Odine finds a way of refining magic from sorceresses and makes it into a usable, consumable form (he invents "para-magic"). This point alone means that they can't be the same world.
That and the fact that the summon monsters look different.
It was just squaresoft making tribute to themselves.