The distinction is important for several reasons: A Mad Scientist and a Quirky Inventor both create outlandish inventions that defy the laws of science, but the differences lay in how the invention is used. Where the Mad Scientist uses his inventions to gain power for himself or to prove someone wrong, the Quirky Inventor is more apt to use his science to help people or, in the more naive examples, believe that he's helping people.
A good example of a Quirky Inventor is Doctor Emmet Brown from the Back to the Future movies. His time machine was invented because he came up with the idea and wanted to see if he could make it work. The intentions behind the Delorian time machine were innocent -- building the device only -- but the end result of how it was used became the central conflict of the movies. Even at the end of Back to the Future, Part III, the steam-powered time train was created so Marty wouldn't worry about Doc and Clara.
By contrast, a standard Mad Scientist is someone like Doctor Moreau from H.G. Wells's The Island of Doctor Moreau. According to TVTropes.org, one of my all-time favorite websites:
"The titular vivisectionist isn't as early as Frankenstein, but he played a major role in shaping the trope. He had Einstein Hair - decades before Einstein. He had the Mad Scientist Laboratory - his island (and he likely brought tropical island laboratories into vogue). Cast out from society, with only one assistant? Oh, yes. He did it all For Science but used extremely painful methods that would give any PETA representative nightmares. Turned on by his own creations? Of course. Several films adaptations even give him a beautiful daughter of his own creation. He also provided the beginnings of the Reluctant Mad Scientist - he never intended to get revenge on the other scientists who cast him out, and in his own mind he had noble purposes for his work; it's only his (possibly willful) ignorance of how torturous his methods are that makes him less than a sympathetic character."For non-literary examples of the proper Mad Scientist, who is completely unrepentant and uncaring about who his science hurts, you don't have to look much farther than the Doctor Who series. Davros, who created the evil race of Daleks, is the prime example of the maniacally evil Mad Scientist who uses his brain power to further his own twisted goals.
Steampunk is rife with Mad Scientists. There's Doctor Cornelius Hyde in Arthur Slade's The Hunchback Assignments, Professor Minnericht in Cherie Priest's Boneshaker, the Hypocras Club/Order of the Brass Octopus* from Gail Carriger's Parasol Protectorate series, and John Scared in S.M. Peters's Whitechapel Gods to name a few. Wacked-out inventions that run on steam power or clockwork mechanics, strange uses of biology to develop new creatures, genetic anomalies made even weirder in the gaslight. Steampunk is very much the playplace of the mad scientist.
Take these madmen of science though, and give them a heart. Give them remorse and an aim to better the situation of their fellow man. Then you have a Quirky Inventor. He may have the same insane devotion to SCIENCE that the Mad Scientist does, but the difference is that the Quirky Inventor has a morality that essentially forces him to follow some variation on the Hippocratic Oath. Distilled down to its essence, the Quirky Inventor is a Mad Scientist who uses his brilliance for good and not for evil.
What other examples of Quirky Inventors or Mad Scientists do you know of in fiction or in real life?
NOTE: I avoided talking about Victor Frankenstein, the eponymous doctor of Mary Shelley's seminal novel, because he's an unique case in fiction -- many Mad Scientists don't reject their original aims like he did, which is the point of that story.
* Gail Carriger gave me the correct name of her Mad Scientist group on Twitter earlier this evening. Hence you see the correction.