Frenetic comes from Greek phrenitis (brain inflamation/insainity) via Latin phreneticus and old French frenetike, meaning "mad" or "delirious", eventually evolving to describe wild, energetic, or chaotic activity, sharing roots with frantic and phrenology (mind/skull study). The core idea links to a "mind" (phrēn) affected by inflammation or madness, moving from a medical term to a descriptive one for wild excitement. 

The difference between frenetic and frantic is that frenetic means wildly energetic, fast, and almost uncontrolled, often with a hectic but productive vibe (like a busy city); frantic means desperate, wild with panic, fear, or distress, implying chaos and negative agitation (like someone searching wildly for a lost child).  While both suggest high energy, frenetic leans towards intense activity, whereas frantic implies emotional distress and disorganization). 

According to the Oxford English Dictionary (OED), the word frenetic first appeared in English during the Middle English Period (1151-1500), with the earliest known use found in a translation by John Trevisa from before 1398, meaning "temporarily deranged, delirious, crazed," stemming from Old French and Latin roots for mental derangement. 

Examples of "frenetic" used in a sentence: 
Describing pace/rhythm: "The stock market experienced a frenetic day of trading." 
"Trading volumes have skyrocketed, underscoring investors' frenetic attempts to protect their portfolios." 
Describing activity: "The team engaged in frenetic activity to meet the deadline." 
"How often in our frenetic world do we stop to look properly?"
Describing energy/mood: "The concert had a frenetic energy that captivated the audience." 
"There is nothing here that is not familiar, though the pace has become more frenetic." 
Describing movement: "The dancer's movements were frenetic, yet beautiful."  
"The music matches the frenetic movements of the dancers, and Spanish instruments such as maracas and drums are often used for accompaniment."
Describing sound: "The sudden crash was followed by frenetic screams". 
"As the crowd grew the vibe and atmosphere became more intense, the music seemed to become more frenetic." 

Just the facts:

FRENETIC Definition & Meaning - Merriam-Webster

FRENETIC Synonyms: 55 Similar and Opposite Words | Merriam-Webster Thesaurus