The difference between the 'spirit' and the 'soul' is best described in the book:
Man after Death by
Mohammed-Ali Hassan Al-Hilly.
http://www.quran-ayat.com/man/index.htm
Therefore, according to this late interpreter of the Quran and the Bible; he explained it as follows:
The 'spirit' is a general term about every living being has a spirit: the tree has a spirit, the animal has a spirit as that man has a spirit.
While the 'soul' is a term used for man and genie (the intelligent being)
The spirit of man after 40 days of age [when he will have the hearing, the sight and the spiritual heart] is called 'soul'.
So the 'soul' is limited for man not for animal or plant: e.g. you can say the spirit of a tree, but not the soul of a tree .. the spirit of an animal, but not the soul of the animal.
But we can say: the soul of man and the soul of genie.
In fact, all spirits and souls are formed from the 'ether' not from the matter, while the body is created from the material substances.
http://www.quran-ayat.com/man/index.htm#The_Soul_
quran-ayat.com/man/index.htm#The_Soul_