Difference between weak and strong AI I'm trying to understand the difference between weak and strong AI. For an example, let's say we would pass the turing test - would it show strong AI or weak AI then?

I don't believe that this is standard terminology, but more philosophical. It was mentioned  by John Searle in his "Chinese room argument". As I understand, strong AI is about computers really being intelligent such as having a mind and thus a conciousness, and weak AI refers more to computers being able to simulate the behaviour of human intelligence on only specific problems (think chess, etc.)

Now, the question is - if we would be able to pass the turing test, would it be called weak or strong AI then? Could it be strong AI due to the fact that the turing test is not limited to a certain area or a specific problem?

I came across it on wikipedia: http://en.wikipedia.org/wiki/Chinese_room
The usual distinction is that strong AI, also known as artificial general intelligence, refers to systems that can perform arbitrary tasks requiring intellect, whereas a weak AI is only able to perform specific intellectual tasks.  So, for example, a computer chess program or a system that was able to compose interesting music would be a weak AI, since it only does one thing.

Passing the Turing test would indicate something close a strong AI. Although one could argue that it only requires performing a specific intellectual task (i.e., conversation), that conversation could range over just about anything that humans can intellectualize about.  Indeed, the Wikipedia page I linked above mentions the ability to pass the Turing test as a component of an operational definition of strong AI.