We are indeed tripartate, as your post showed, Rome.
What is the difference between soul and spirit? If we identify the soul as nephesh, or the breath of life, as the Bible does, and understand that the 'higher' animals also have it, then we can see that whatever the difference is between us and them is probably related to the difference between soul and spirit.
We have individuality, personality -- so do they.
We can learn from others -- so can they.
We can form bonds of attachment with other sorts of animals -- so can they.
We can have desires independent of our needs -- so can they.
But we are far more than that, which is probably connected with nephesh, or the soul.
We can reason abstractly.
We can appreciate beauty for its own sake.
We can communicate with abstract language which uses abstract terms for abstract thoughts.
We can plan, consciously, for the distant future.
We can record the past, and read it.
We often focus on expressing our individuality.
We are intensely creative.
There is more, but I think you can get the idea. These things I would personally identify with spirit.