Assault is a common law crime, and while common law offenses cannot be recognized at the federal level (US v. Hudson and Goodwin, 11 U.S. 32), the states may abolish them or not. Massachusetts recognizes common law offenses, as well as General Laws offenses. The exact meaning of "assault" emerges from centuries of usage under law, and the crime of assault is not different from the tort of assault. The Restatements of Torts have suitable definitions of battery and assault, so that there isn't vast leeway to define a scowl as an assault. Drawing on these various definitions "out there", Massachusetts conveys the essential concepts to a jury in the form of instructions, saying
An assault may be committed in either of two ways. It is either an
attempted battery or an immediately threatened battery. A battery is a
harmful or an unpermitted touching of another person.
There is further elaboration (via jury instruction) here. In Commonwealth v. Burke, 390 Mass. 480, the court says "Our analysis demonstrates, by recourse to the common law, that a physically harmful touching is a battery, and consent is immaterial"; that is, the definition comes from the common law, not a statute (the penalty, though, comes from statute). Not all crimes are defined in common law, such as failure of a sex offender to register, which is criminalized in G.L c. 6, §178h(a).
The general scheme for the tort of battery is a bit convoluted, because it amounts to any touching, unless permitted, at which point there are a number of conditions that constitutes "being permitted". Self defense is one of those. Rather than build "self defense" into the definition of "battery", "battery" is left very simply, and the law prohibits unpermitted battery. The Massachusetts model instructions for self defense are here, again summarizing a few centuries of wisdom over what is and is not proper self-defense. A clear example would be that it is not self defense to intentionally kill a person who blocks your passage through a doorway. One of the conditions for using non-deadly force is that the Commonwealth must prove that "the defendant did not reasonably believe he (she) was being attacked or immediately about to be attacked, and that his (her) safety was in immediate danger"; they must also prove that you "did not do everything reasonable in the circumstances to avoid physical combat before resorting to force"; and "that the defendant used more force to defend himself (herself) than was reasonably necessary in the circumstances".
You can compare this to Washington state law which has a statutory statement of "self defense", which says that force is not unlawful
Whenever used by a party about to be injured, or by another lawfully
aiding him or her, in preventing or attempting to prevent an offense
against his or her person, or a malicious trespass, or other malicious
interference with real or personal property lawfully in his or her
possession, in case the force is not more than is necessary
This results in a particular set of jury instructions that correspond in various ways to the Massachusetts instruction; though I don't want to imply that they are the same. The Washington instruction refers to
such force and means as a reasonably prudent person would use under
the same or similar conditions as they appeared to the person, taking
into consideration all of the facts and circumstances known to the
person at the time of [and prior to] the incident.
which is another way of slicing up the elements of the Massachusetts self defense defense.