The following questions are entirely based on the corresponding article from Wikipedia.
The assumptions of both laws are the same, and the strong law has a more general claim than the one of the weak law. The question is then: what is the reason for keeping them separated? Why do they always presented as two distinct results? If we assume the same, why would we wish to restrain what we get? Probably, I just do not really realize how the two laws are being used.
Also, there is the following statement under Weak law:
Convergence in probability is also called weak convergence of random variables.
Is not it about convergence in distribution?