I am just now learning about these, and I have seen them defined as follows: The generating functional for a set of fields $\phi_i$ is defined by:
$$Z[J_i]=\int\mathcal{D}\phi_i e^{i(S[\phi_i]+\int J_i\phi_i)}$$
and the partition function is $Z[0]$, generating the vacuum bubbles. However, as I read more and more about this, I find the semantic distinction between "partition function" and "generating functional" upheld less and less. Many people, such as Wikipedia, equate the two and just call everything "the partition function".
Does anybody have any particular knowledge about how important the semantic distinction between the two is at higher levels (i.e. further down the line in QFT, or in certain lines of research, or...)?