Frantic and frenetic share a common etymological source — along with frenzy and words associated with psychiatric conditions and a discredited pseudoscience — but the adjectives differ in connotation.
The words derive from the Greek noun phrenitis, meaning “inflammation of the brain.” Phrenetikos, the adjectival form, was borrowed into Latin as phreneticus, which led to the Old French word frenetik. Both frantic and frenetic derived from the French term, with a divergence of meaning. Although they can be used interchangeably, frantic implies severe agitation in a distraught state, whereas frenetic suggests excessively energetic or fast-paced activity.
The adverbial and nominal forms of frantic are frantically (originally franticly) and franticness, and those of frenetic are frenetically and freneticism. Frenzied is the adjectival form of frenzy. Archaic forms for frenetic (phrenetic) and frenzy (phrenzy) appear rarely.
The noun frenzy, cousin to frantic and frenetic, originally meant “delirium” or “insanity,” but though it technically refers to temporary madness or to violent agitation, the modern sense is mostly likely to be more casual, referring to intense behavior, such as in the phrase “feeding frenzy,” associated with the unrestrained eating habits of sharks, for example. (By extension, that phrase now has a figurative sense of numerous people criticizing or taking advantage of a vulnerable person or organization.)
The basic Greek root, phren- (meaning “diaphragm” or “mind”) is seen in various psychiatric contexts. Phrenic means “pertaining to the diaphragm or the mind” and is rare in lay usage, but most people are familiar with the suffix –phrenia (meaning “mental disorder”), best known in the noun schizophrenia and the adjective schizophrenic (the latter often used loosely to refer to inconsistent behavior).
What’s the connection between diaphragm and mind? In classical times, the diaphragm, adjacent to and associated with the heart, was considered the seat of emotions, and the brain was considered the seat of thought, so they were thought to be analogous.
The Greek term was also applied to phrenology and associated words referring to a pseudoscience in which measurements of the skull supposedly indicated the strength of certain mental faculties and personality traits. Though the precepts of phrenology have long since been considered outside the realm of proper science, they are echoed in neurological theories about how various parts of the brain carry out different functions.