mav, perhaps the legal definition is more carefully circumscribed. I'll re-check the law dictionary tonight, but as I recall from this morning:
Assault is in rough terms the threatening (not necessarily consummated) of a physical attack, thus the "putting the other party in fear". (The harm threatened must be physical harm to the person, not to his property, feelings or reputation.) As you note, the threat may be conveyed either physically (the raised fist) or verbally ("I'm gonna kill you"). The threat, even if not consummated, can be used to coerce or extort. Indeed, even if the attacker is merely bluffing, with no intention to follow through with his threat, he commits assault by striking fear into the heart of the other party. (Note that by virtue of the above, "assault" is not synonymous with "attempted battery".)
Battery is the implementation of that threat -- or, without any warning threat, the actual doing of physical violence to the person. The general wisdom, perhaps not 100% accurate, is that a battery always includes an assault, but not vice versa.
EDIT: I am speaking only of the common law definition. Indivdual states and other political jurisdictions each have specific and varied definitions.
