These are separate and distinct intentional torts. Blame the Media, not yourself. The "4th Branch" seldom (never?) grasps the dichotomy.
An Assault occurs when a Plaintiff justifiably (reasonably) fears imminent harm by the Defendant despite the fact there has yet to be physical "contact".
When, and if, a material and unwelcome "contact" is made, the Assault morphs into a Battery. Moreover, an "accidental touching" cannot be the basis of an intentional wrong. If the Defendant's act was accidental, it was not consciously or subconsciously intended.
Moreover, your question raises some esoteric questions worthy of further analysis:
(1) Is there any such thing as any attempted Tort?
(2) Might the analysis be different if the Assault lasts but a couple of seconds before the Defendant lands a punch?
(3) Why does the Media consistently get this wrong?
(4) What is an "unwelcome" touching?- is the test an objective or subjective one from the perspective of the Plaintiff?
(5) Consider an unlawful and serious non-consensual "touching" in the context of the egg-shell skull theory. Does the Plaintiff suffer from Hemophilia?
(6) What are the Plaintiff's damages in the event of an insignificant, though cognizable, touching?
(7) In considering point #6, above, what are nominal damages?
(8) Is one dollar of actual damages sufficient to support an award of punitive damages?
(9) Subject to statutory caps (and all else being equal), is an award of punitive damages available whenever an intentional tort gives rise to a well-pled claim for relief?
*Remember the traditional algorithm for Punitive Damages: An award of "smart money" sufficient to punish and deter, but not so large as to bankrupt the Defendant.