Many of you may be confused by that opening title statement... but it is true, we all have spirits but we don't have souls [at least, no one can prove we have souls].
Both terms are quite similar, and both terms can come to mean many different things.
What's the difference?
Well I focus on the Dictionary.com's first and primary definition for each statement.
"Soul - the principle of life, feeling, thought, and action in humans, regarded as a distinct entity separate from the body, and commonly held to be separable in existence from the body; the spiritual part of humans as distinct from the physical part." - Dictionary.com
"Spirit - the principle of conscious life; the vital principle in humans, animating the body or meditating between body and soul." - Dictionary.com
Quite clearly, Spirit and Soul are different words and refer to different things, at least they do the way I use them.
A "soul" is a consciousness or living entity that lives separate from a human body during life [using it as a shell] and apart from it after death. - There is NO evidence whatsoever that this thing exists at all.
So, no, I do not believe I have a soul.
Christians [and laymen] sometimes get "soul" and "spirit" mixed up. - Probably because "spirit[s]" [the plural] can sometimes refer to multiple incorporeal entitities, but that is not the kind of "spirit" I am referring to.
Rather, in my definition, a "Spirit" is the human's personality that is made up of any number of internal and external influences. While this is almost the same definition as a "soul." One should be careful in making the assumption that it IS the same, because it's not.
Unlike a "Soul" a person's "spirit" [the essence of their "self"] is not living apart form their physical body... it is a part of it. It is the combination of body to brain, brain to body, and brain to brain communication that tells the person "this is who I am" and gives them all their thoughts, ideas, memories, and perceptions of the world around them. The Spirit is "run" by the brain, like electricity is powered by a generator. Unlike a soul, when the brain dies, the spirit dies too.
To deny that I have a spirit, is to deny that I have an identity, a personality, a sense of self.
But to assert that I have a soul, is to go beyond the boundaries of my knowledge and either become naively delusional, or out-right lie.