Adding some detail to the accepted answer by <PERSON>.
TL;DR version:
Similarities between <PERSON> and <PERSON>:
* <PERSON> was explicitly intended to replace <PERSON> in <PERSON> rogue's gallery.
* <PERSON>'s costume and weapons are based on those of the Green Goblin.
* The versions with super-powers have generally had the same powers (enhanced strength, speed, agility).
* Both have <PERSON> as their primary opponent.
* Both have had a number of people take on the name, though the first to use each name is the one most strongly associated with it.
Differences: The most notable difference may be that most versions of the <PERSON> have been sane, while most versions of the Green Goblin have been insane.
To provide a bit more detail on the characters from the comics:
The Green Goblin first appeared in AMAZING SPIDER-MAN #13 (July 1964). His origin and identity weren't revealed for a couple of years (issue #39-40).
The original Green Goblin was <PERSON>. His mind was affected following a chemical accident at his company, basically causing him to have a split personality: <PERSON>, the father who may have been a bit too occupied with his business, and the <PERSON>, the evil criminal mastermind. Before the revelation of his dual identity, <PERSON> and <PERSON>'s son <PERSON> met at college, and eventually became best friends.
Over the next few years, <PERSON> was mostly the busy businessman and father, with occasional returns to being the <PERSON>. In (what was at the time) his next-to-last appearance, seeing <PERSON> in danger following a drug overdose shocked him from the <PERSON> back to <PERSON> (issue #98, July 1971).
About 2 years later, <PERSON> again became the Green Goblin (issues 121-122, June and July 1973). This was the story where he killed <PERSON> then-girlfriend, <PERSON> (in 121), then inadvertently killed himself (he tried to attack <PERSON> by using his remote to steer his Goblin Glider, which was damaged and had a sharp piece of metal sticking out; <PERSON>'s spider-sense warned him something was up, and he dodged - which left <PERSON> right in the path of the glider, which hit and killed him (or so we believed at the time)).
Following his father's death, <PERSON> had a breakdown. His grief over his father, combined with his inadvertent discovery that <PERSON> was <PERSON> (and, probably, <PERSON>'s incipient relationship with <PERSON>'s ex-girlfriend, <PERSON>), combined to drive <PERSON> crazy. He located a cache of his father's <PERSON> equipment, and attacked <PERSON> as a new Green Goblin (issues #136-137, September and October of 1974). <PERSON> was locked away for a short while, received therapy, and returned with no memory of <PERSON>'s identity.
Unfortunately, his therapist, <PERSON>, upon learning about all that happened with <PERSON>, took advantage. He got <PERSON> to reveal the location of one of his father's stashes of equipment, and became the third Green Goblin (issues 176-180, January-May of 1978). Under the circumstances, it's assumed that this is <PERSON> until the end of the story. 167
To the best of my knowledge, <PERSON> has not been seen again (and certainly has not taken over the Green Goblin role again). <PERSON> resumed his identity as the second <PERSON> long enough to stop <PERSON>, then forgot about it again. (Note: this was when he fell in love with <PERSON>, his wife until his apparent death years later).
A quick sidebar: when <PERSON> related the Goblin's origin, he notes that he was trying out a formula he'd taken from a former business partner, which exploded. He was apparently hospitalized for weeks, undergoing multiple surgeries to save his life. According to the surgeons, the explosion caused brain damage that was too deep for an operation to reach. <PERSON> claimed he wasn't brain damaged: "... the accident made me more brilliant than I had ever been!" He also claimed that he was "... stronger ... smarter ... tougher than anyone else!"
In context, this is almost certainly his insanity talking. In his encounters with <PERSON>, he generally doesn't seem to be a physical equal to <PERSON> - he relies on weaponry to even the odds against <PERSON>'s powers. 86