Hi,
According to UBC code
Soft story = the story which the latteral stiffness is less than 70% of the stiffness of the story above.
Weak story = the story which the story strength is less than 80% of that the story above.
For more detail, please see in UBC code table 16L
This is Excerpt of definitions given in table 16-L of UBC as OAP said.
Soft story is in which the lateral stiffness is less than 70 percent of that in the story above or less than 80 percent of the average stiffness of the three stories above.
A Weak story one in which the ratio of the story strength to the story shear is less than 80 percent of that in the story above. the story strength is the strength of all seismic-resistant elements sharing the story shear of the direction under codition.