VonC's answer is more to the point, but I just can't resist the urge to post this Venn diagram: Image credit.
english.stackexchange.com/users/300/RegDwigнt
The most probable term would be "geek", as in "computer geek" (roughly "computer whiz").
(not the US geek from fifty years ago, as the lowest form of circus performer, who did horrible, demeaning things).
Even though a geek is not necessarily smart or into computers, but can be in general a "weird person", the only usage of geek I know in French culture is related to computer.
This thread mentions : "Nerd" has several meanings/usages.
One is that of a studious intellectual, meant to be negative but carrying a whiff of envy.
The other is "awkward pain in the neck".
One (non-official) difference between nerd and geek (in the computer field) could also be in term of general activity: "Nerd" = producer "Geek" = consumer Eg.
a nerd creates video games, a geek plays the video games.
But those two terms certainly cannot be limited to this simple interpretation.
That being said, I thought the remark from John Hodgman was quite accurate:
Comedian John Hodgman recently spoke at a Washington DC press dinner, following Barack Obama, touting Obama as the first Nerd President, since Obama had admitted to collecting comic books and being a fan of Star Trek.
Obama's Nerd intellectualism was contrasted to the "Jock" mentality that had defined the Bush years.
In the midst of this speech Hodgman suddenly referred to Obama as a geek, quickly adding this aside: "And to those who say, 'Wait, there's a difference between nerds and geeks,' I answer, 'Shut up, nerd!'" Nicely illustrated by phdcomics :
english.stackexchange.com/users/110/VonC
Obligatory xkcd reference :
english.stackexchange.com/users/303/Steve Melnikoff
Geek or Nerd = People who are passionate about something and laughed at by people who are NOT willing to take the time or effort find something to be passionate about and in fact trying their best to poke fun at people who care about something :-)
english.stackexchange.com/users/None/
Merriam-Webster defines them thusly:
Geek - an enthusiast or expert especially in a technological field or activity Nerd - one
slavishly devoted to intellectual or academic pursuit
I'd say they're virtually synonyms.
I've certainly heard them used interchangeably.
english.stackexchange.com/users/1914/Joshua Karstendick
My definition of a Geek is that its somebody that is very interested in something and knows a lot about that subject, but also knows a lot or just as much about many other subjects.
ie computers AND maths AND physics AND chemistry AND politics.
A Nerd however goes VERY deep on one subject and has a cursory interest in other subjects.
What this means is that geeks do some really interesting things in some fields, and manage to cross fields really easily.
But the focused advances in most fields come from the hardcore Nerds.
Thus a Nerd is a very hardcore focused Geek.
english.stackexchange.com/users/2067/Mark Underwood
A theory of a hierarchy, based on level of social interaction capabilities, has been discussed over numerous, excellent bottles of beer.
"Geeks," "nerds," and "dorks" all have the same level of passion for their field of study.
As a result, it is impossible to distinguish among them based on their level of skill and degree of interest.
Instead, it was concluded, one night, that it was better to organize them by their social skills.
"Geeks" have a high level of social skills and are able to interact with people outside their area of expertise: they might be geeks in, say, Ruby on Rails programming, but they can chat up an art historian with alacrity.
Nerds, on the other hand, are less comfortable outside their circle of peers--a C# programming nerd can talk to an advertising sales rep,
if he/she must, but only if there is a substantial amount of alcohol involved.
For those unfortunate people who are so absorbed in their subject matter as to consider social interaction with anyone beyond their ken...
we tend to call them dorks.
It's an cruel classification, but it exists all the same.
A fourth class have been discussed, usually late into the drink, and it's the question of the "poser," or someone who thinks they are an expert in something and think they belong in the "geek" or "nerd" class.
Even "dorks" agree that the proper term for them is probably "dweeb."
english.stackexchange.com/users/5683/logosamorbos
Someone reasonably famous once said "Nerds are simply Geeks who earn lots of money
" I think it was in the context of Bill Gates.
english.stackexchange.com/users/2066/MrFidge
Which term correctly identifies those who enjoy and are involved with programming and technology,  geek  or  nerd ?
Which term correctly identifies those who enjoy programming/technology: "geek" or "nerd"?
english.stackexchange.com
<word-choice><nouns><terminology>
english.stackexchange.com/questions/4823
english.stackexchange.com/users/2019/Moshe
Whilst it is possible that these terms are virtually synonyms and interchangeable, "Geek" is probably the more common in this context. The most likely term is "geek" meaning "computer geek" and not the circus performer referred to fifty years ago.A "nerd" is someone who creates "video games"; a "geek" is someone who plays them. It can mean people passionate about something who are mocked by others. The difference is that a nerd has very deep interest in a subject, but a "geek" would have some skills in certain areas but have skills that can apply to many areas.There is no distinction.The joke about the difference is that one earns more than the other. 
Whilst it is possible that these terms are virtually synonyms and interchangeable, "Geek" is probably the more common in this context. A geek  is an enthusiast or expert especially in a technological field or activity. But,"Geeks" still have a high level of social skills and are able to interact with people outside their area of expertise. A nerd is someone who is slavishly devoted to an intellectual or academic pursuit and nerds are less comfortable outside their circle of peers. Comedian John Hodgman recently spoke at a Washington DC press dinner, following Barack Obama, touting Obama as the first Nerd President, since Obama had admitted to collecting comic books and being a fan of Star Trek. You could say that a Nerd is a very hardcore focused Geek.
Geek and nerd are virtually synonyms and are used interchangeably. Whilst it is possible that these terms are interchangeable, "Geek" is probably the more common in this context.
The most likely term is "geek" meaning "computer geek" and not the circus performer referred to fifty years ago. A "nerd" is someone who creates "video games"; a "geek" is someone who plays them. It can mean people passionate about something who are mocked by others. The difference is that a nerd has very deep interest in a subject, but a "geek" would have some skills in certain areas but have skills that can apply to many areas.
A geek  is an enthusiast or expert especially in a technological field or activity. But,"Geeks" still have a high level of social skills and are able to interact with people outside their area of expertise. A nerd is someone who is slavishly devoted to an intellectual or academic pursuit and nerds are less comfortable outside their circle of peers. Comedian John Hodgman recently spoke at a Washington DC press dinner, following Barack Obama, touting Obama as the first Nerd President, since Obama had admitted to collecting comic books and being a fan of Star Trek. You could say that a Nerd is a very hardcore focused Geek. Someone reasonably famous once said "Nerds are simply Geeks who earn lots of money
"Geek" is possibly the more common term in this context. It is possible that these terms are interchangeable.