In the second case, the items are not alternative expressions of the same underlying construct but are understood to represent different constructs that share variance with each other. One conducts this type of factor analysis in order to identify dimensions that describe which constructs tend to covary most highly. In this case, the factor does not represent a single, definable construct; it represents variance shared among a set of constructs. There is no reason to think that two individuals with the same score on this kind of factor are the same on the factor's constituent constructs.
