Going by "Integrity = Validity + Completeness", I use the following terminology:
- Data validity testing - checking that all of the data you have is correct
- Data integrity testing - checking that all of the data you have is correct and all of the data is there
Although the previous citation uses validity and completeness in the context of relational databases, I use those terms for any sets of data, whether they're extracted/transformed/loaded from a database, or simply in regular files. Furthermore, I refer to a particular rule that holds true for a particular set of data as a "data invariant."