what ff7 has lifestream from is the Gaia theory, which is an actual theory, thought up before final fantasy, even though final fantasy uses the gaia theory alot in most of their games, the most know being of course the whole ff7 armada XD
however, I'm using the gaia theory as what it is, the gaia theory, not a playoff of final fantasy's version =3
gaia means earth in greek XD
Anima is the Latin word for Lifeforce XD
The Terrestrials are the animals only =D
humans are a gianormous mix of pretty much EVERYTHING now, though they ended up with more terrestrial components =3
elementals actually prefer to exist in their elemental form, though the condence to a 'human' (though in actuallity, it's based on a sorta default base that was created, and which the humans are most like, so on so forth...i can talk about that for a while XD) form to converse with others, and so forth.
I should make note my elementals are far far away from most normal versions of elementals
Essential Terra Flares in the lifestream (sorta like solar flares XD) at the begining of Terra created initial Anima. However, being pure, they automatically latched onto the first living being they encountered and absorbed some of their qualities.
At the time Anima were created, the only other creatures on Terra were the Terrestrials
The theory for now is some unknown greater beings, perhaps some form of extreme Mystic, created the Terrestrials out of the materials already found on Terra.
They(the plants) used Quintessence to bring the initial creatures to life; small smecks of quitessence occasionally landed on Terra, causing the birth of all plant life, which are the only beings that can convert impure Quintessence (solar energy, because stars are made of Quintessence), into Terrestrial material.
The also brought with them the four Elements with them (fire, water, air, earth) which merged with the remaining terra materials, giving them various properties.
where too much of one element condenced, elementals were formed.
at this point, Terra's lifeforce was very near the surface of the planet, as it had not yet receded to the core, so occasionaly 'spikes' in the lifeforce would also condence, forming pure Anima.
now, after all this had happened, these greater lifeforms decided that there needed to be some form of guardian to make sure Terra was regulated; however, just like our bodies, It could not be an outside sourse, as Terra would not recognize it.
So the greater lifeforms took bits of pure lifeforce and creater humans, without bias or anything else, to run the works of the planet.
http://en.wikipedia.org/wiki/Gaia_theory^ what I'm going by is the section that says that the earth is an entire life system, including all the organisms that live on it, collectivly called gaia.
not a very indepth article, but it gives an overveiw