A lengthy quotation provides the relevant data:
The will, and the affections of the soul, are not two faculties; the affections are not
essentially distinct from the will, nor do they differ from the mere actings of the will, and
inclination of the soul, but only in the liveliness and sensibleness of exercise.
It must be confessed, that language is here somewhat imperfect, and the meaning of words
in a considerable measure loose and unfixed, and not precisely limited by custom, which governs the use of language. In some sense, the affection of the soul differs nothing at all from the will and inclination, and the will never is in any exercise any further than it is affected; it is not moved out of a state of perfect indifference, any otherwise than as it is affected one way or other, and acts nothing any further. But yet there are many actings of the will and inclination, that are not so commonly called affections: in everything we do, wherein we act voluntarily, there is an exercise of the will and inclination; it is our inclination that governs us in our actions; but all the actings of the inclination and will, in all our common actions of life, are not ordinarily called affections. Yet,what are commonly called affections are not essentially different from them, but only in the degree and manner of exercise. In every act of the will whatsoever, the soul either likes or dislikes, is either inclined or disinclined to what is in view: these are not essentially different from those affections of love and hatred: that liking or inclination of the soul to a thing, if it be in a high degree, and be vigorous and lively, is the very same thing with the affection of love; and that disliking and disinclining, if in a greater degree, is the very same with hatred. In every act of the will for, or towards something not present, the soul is in some degree inclined to that thing; and that inclination, if in a considerable degree, is the very same with the affection of desire. And in every degree of the act of the will, wherein the soul approves of something present, there is a degree of pleasedness; and that pleasedness, if it be in a considerable degree, is the very same with the affections of joy or delight. And if the will disapproves of what is present, the soul is in some degree displeased, and if that displeasedness be great, it is the very same with the affection of grief or sorrow.
Such seems to be our nature, and such the laws of the union of soul and body, that there
never is in any case whatsoever, any lively and vigorous exercise of the will or inclination of the soul, without some effect upon the body, in some alteration of the motion of its fluids, and especially of the animal spirits. And, on the other hand, from the same laws of the union of the soul and body, the constitution of the body, and the motion of its fluids, may promote the exercise of the affections. But yet it is not the body, but the mind only, that is the proper seat of the affections. The body of man is no more capable of being really the subject of love or hatred, joy or sorrow, fear or hope, than the body of a tree, or than the same body of man is capable of thinking and understanding. As it is the soul only that has ideas, so it is the soul only that is pleased or displeased with its ideas. As it is the soul only that thinks, so it is the soul only that loves or hates, rejoices or is grieved at what it thinks of. Nor are these motions of the animal spirits, and fluids of the body, anything properly belonging to the nature of the affections, though they always accompany them, in the present state; but are only effects or concomitants of the affections that are entirely distinct from the affections themselves, and no way essential to them; so that an unbodied spirit may be as capable of love and hatred, joy or sorrow, hope or fear, or other affections, as one that is united to a body.
Edwards defines affection as an inclination of the will. He does not equate affection and inclination, however. Any desire of the will that leads to an effect is an inclination, but an affection is an inclination of a higher degree resulting in a more pronounced effect. The key elements of an affection, however, is that it originates in the will as an inclination and is properly understood as being properly seated in the mind or soul (which includes the will).
Edwards then distinguishes affections from passions:
The affections and passions are frequently spoken of as the same; and yet in the more
common use of speech, there is in some respect a difference; and affection is a word that in its ordinary signification, seems to be something more extensive than passion, being used for all vigorous lively actings of the will or inclination; but passion for those that are more sudden, and whose effects on the animal spirits are more violent, and the mind more overpowered, and less in its own command.
Edwards' distinction is not simply one of intensity (though there is that), but also of kind--whereas the affections are seated in the mind, it is the passions that are exhibited more violently in the body to the overpowering of the mind. Although Edwards does not explicitly say so in his treatise on the Religious Affections, the implication of the above quote would be that whereas affections originate in the mind as an inclination of the will, passions circumvent the mind and incline the will toward carnal, bodily ("animal spirits") satisfaction. It seems to be these very same passions, just so defined, that Paul says God gave up corrupted men and women unto the influence of in Romans 1:26, which dominated those under the power of the flesh (Rom. 7:5) and which Christ, through our union with him in crucifixion, has crucified (Gal. 5:24). Indeed, it seems to be the passions that James says, "wage war among in your members" (4:1) and are the source of quarrels and conflicts among the brethren.
For Edwards, then, the affections are not those bodily effects that overpower the mind, circumventing or "surpassing" reason and understanding. Rather, the affections are the inclinations of the will reacting to the truths that are impressed upon the mind and exert the will in affections (such as love, hatred, joy, gratitude, grief, fear, zeal, and so on) that culminate in the right worship of God in accordance with the truth that the mind grasps.
A good, though not infallible, test is to ask oneself whether, in the aftermath of an "emotional experience," whether or not one was aware of any thought. Many times we act out of a strong inclination and reflect, saying, "I don't know what I was thinking!?" Such an answer is more accurate than we may realize, since it probably reveals the working of passions rather than the affections of which Edwards speaks. If one can articulate a reason (and the reason is true rather than pretended) for the inclination and its subsequent action (think here of David's dancing exuberantly down the streets of Jerusalem when the Ark of the Covenant was returned to the city), then it is more probably an affection arising from the soul's exultation in the truth than of a bodily or carnal passion.
In any case, reading Edwards correctly on the affections should motivate more skepticism toward the current state of religious expression in our land than serve as justification for much of what passes for a proper expression of worship.