[twic]

There's an old and frustrating terminology problem here. You mention testing a parser; assuming the parser contains more than one class, or group of functions, i would consider a test of the whole parser to be an integration test, not a unit test.

[bluejekyll]

By parser I mean any small thing that might parse text.

Since I tend to deal with distributed systems, I generally think in terms of blackbox tests as dealing with application APIs rather than function APIs, and integration tests as multiple system components being tested together.