Intuitive test case investigation makes use of the intuition and experience of the tester, e.g. due to errors that have occurred in the past, or the testerís suspicions where the faults could possibly occur. The tester supplements the corresponding test cases to reflect such situations.That intuitive test case investigation should not be used as the primary test procedure, but rather serve as a supplement to the systematic test procedures.
It isn't exploratory testing, though, unless it's simultaneous test design, learning, and test execution. I would contend that "Intuitive test case investigation" is heuristic-based testing. Heuristics can look like intuition if the person using them (or if the person watching) isn't conscious of what those heuristics are.
I would further suggest that all test case investigation makes use of the intuition and experience of the tester, and that all testing is systematic; that is, it is based on some kind of a system. The novice tester may not be using heuristics or experience that we normally associate with testing, but every tester brings something to the table. Even the novice tester has some system for testing; it's just that it may not be the most useful or efficient system for the context.
I don't think this kind of testing has anything to do with ESP. It is more along the lines that a tester can observe a screen and intuitively note presentation glitches and basic errors that need not be explicitly defined, such as a clobbered date value. When you specify test cases, you may well group an unspecified number of tests simply by establishing a "review screen presentation" or so work item.
Intuitive should be somewhat obvious, so there is no implication of exploratory testing to observe that something is amiss, although you could start to dig a little deeper and see if that clobbered date is a presentation error or a data error. The "heuristic" context suggested by Michael is a level of familiarization to "know" what to expect (unless the specification states otherwise), just as explained above.
I think even a novice tester uses intuitive tests if only to identify that the system is not quite as intuitive to an end-user as the designers may have planned. In that case the lack of heuristics gives the tester the advantage for determining if the system is inherently user-friendly. From that perspective this can be highly useful.