I've seen both terms being used in papers and it seems to me they essentially mean the same thing referring to three generations of leptons and quarks as families. Is this true or are there some differences between the two terms.
Are Generations and Families of elementary fermions one and the same?
Yes. In the context of the Standard Model, "generation" and "family" mean the same thing. They both refer to a group of fermion fields having the same pattern of couplings to the gauge fields: strong, weak, and electromagnetic.
From page 3 in Donoghue et al (1992), Dynamics of the Standard Model:
One of the more striking aspects of the Standard Model is the apparent redundancy in the total number of quarks and leptons. There are three generations (or families) of these particles...
By the way, although the couplings to the gauge fields are the same in each generation/family of fermions, their couplings to the Higgs field differ. In fact, the Higgs couplings slightly mix the different generations/families with each other.