There are different views on this, 1 - man is a bi-part being (Soul/Spirt - flesh); and 2 - man is tri-part being (Soul, Spirit, and flesh).
I hold to the later due to how scripture distinquishes between them at times but it is important to remember that they are used interchangably just as often. One of the most notable verses in scripture which establish the distinction of the two NOT being the same specific thing is found in Heb 4:12, as the Word of God is powerful..even to the dividing of the soul and spirit...
Here is John Gill on the subject (there are others of this same mind but his is easiest to get to at the moment):
...the apostle seems here to have respect to the several names with which the soul of man is called by the Jews, נקש רוח ונשמה, "soul, spirit, and breath" (p); the latter of these, they say, dwells between the other two. Some by the soul understand the natural and unregenerate part in man, and by the spirit the renewed and regenerate part, which though sometimes are not so easily distinguished by men, yet they are by Christ; others think the soul designs the inferior faculties, the affections; and the spirit the superior ones, the mind and understanding; but the apostle's meaning seems to be this, that whereas the soul and spirit are invisible, and the joints and marrow are covered and hid; so sharp and quick sighted, and so penetrating is the divine Word, that it reaches the most secret and hidden things of men: and this sense is confirmed by what follows,.. and is a discerner of the thoughts and intents of the heart;...
Now he is neither advocating one view or the other here but is speaking simply to the fact they are and does not dismiss either view out right. Another verse which displays this distinction is 1 Thes 5:23.
The terms soul and spirit are used interchangably for the referencing a person or their very being, this is so because they are the same in essence and being but they are each unique and distinct much like the Trinity. To say it more simply - They are the same in essense and being yet each is distintly different. However God can seperate from Himself and All parts still function yet maintain still the essense and being (as Jesus, but we can not (take death) Though the Godhead can seperate and each still continue and function we can not. If our spirit/soul (or spirit and soul - either way you wish to view) leave our body, the body dies as it can not maintain or function of itself. The same is to be said of our soul and spirit.
Now about the Soul and Spirit:
SOUL: The Soul stands for the personal life or for the idividual. It has and conveys emotion (Jer 31:25) and it wars against the lusts of the flesh (Rom 8:16) It is interesting to note the Soul is most ascribed as man's emotional center and place of desire (ie. His soul was in anguish, it vexed his soul ect...) It is also seen refered to as the base 'animal life' again moved primarily by or because of emotion.
SPIRIT: The spirit is related to the higher aspects of man (Rom 8:16 - The Spirit bares witness with our spirit... John 4:23 - we worship God in spirit and in truth). We know that all men have a spirit and that like the flesh the spirit too may also be corrupted (2 Cor 7:1), in light of this verse we have an understanding of why we must renew our minds due to corruption (Rom 12:2) that 'can' take place.
Though a distinction can be noted from the scriptures concerning the spirit and soul, it must also be noted they are facets of the same being (spiritual man) and therefore can be and are interchangably used when speacking of the person as a whole. However what must also be noted is word that is used (spirit/soul) in conjuction as to when the person is in/or doing an action. This is due primarily the fact that the word used speaks to the basis or motivation for which certain or specific types action are done (of intelect or emotion).
Heart: is most often in scripture associated with the soul since it is the core of our desire and the large concept of all of the facets of mans immaterial nature. This is synonymous with the physical center of life and our spiritual core also regarding life.
Mind: is most often in scripture associated with spirit as it is the facet of mans immaterial nature where understanding is centered. This is also synonymous with the physical mental center of intellect and our spiritual faculty with regard to understanding and insight and can be hindered (darkened or dead to truth) or grow (enlightened or made alive with truth now understood.)
Lastly, to sum up MY VIEW - I believe they are united as one entity (inseperable from the other) though they are two seperate aspects of that same being.