(Merely) De facto underdetermination. The thesis does not merely assert that the data or evidence actually at hand happens to leave the theory underdetermined. That certainly may happen, especially when new theories are emerging. In other cases, sometimes real, sometimes contrived, it may be very hard to procure the requisite evidence. The underdetermination thesis is much stronger. It asserts that in all cases, no matter how long and ingeniously evidence collection may proceed, the underdetermination will persist.
(Merely) Sporadic underdetermination. The thesis does not merely assert that there can arise cases, either contrived or natural, in which some part of a theory transcends evidential determination. Such cases clearly can arise. Lorentz insisted that there was an ether state of rest, even though Einstein's work in special relativity made it clear that no observation could determine which it was of all the candidate inertial states of motion. The underdetermination thesis is much stronger; it asserts that all theories are beset with this problem.
Humean Underdetermination. The thesis is also distinct from the most famous of all philosophical problems, Hume's problem of induction or simply the problem of induction. This is the purported impossibility of providing a non-circular justification of induction. No matter how often we have seen that bread nourishes and fire burns, we cannot infer that they will continue to do so. We beg the question, Hume told us, if we ground our conclusion in the assertion that patterns in the past have continued into the future, for that assertion itself presumes the tenability of induction on patterns. If one accepts Hume's skepticism, no evidence from the past on bread or fire will determine their behavior in the future through justifiable inference. This form of underdetermination has been called "Humean underdetermination" (Laudan, 1990, pp. 322-24). It is distinct from the underdetermination of the underdetermination thesis since it denies the possibility of induction outright as opposed to addressing a failure of the determining power of induction. This form of the thesis trivializes underdetermination. If one denies induction is possible, a fortiori one must deny it any interesting properties such as a power of unique determination.6
Underdetermination by Grue. In Goodman's (1983) celebrated example, our past observations of green emeralds confirm the hypothesis "All emeralds are green." and also equally the hypothesis "All emeralds are grue." where "grue" means "green if examined prior to some future time T and blue otherwise." The problem of grue can be given a narrow or a broad reading. Neither coincides with the underdetermination thesis. In the narrow reading, grue reveals an underdetermination in the import of evidence within a particular class of syntactic theories of confirmation: those that allow an A that is a B to confirm that all As are B, where we are free to substitute anything grammatically valid for A and B. This is a narrow problem for a particular class of theories, solved by various restrictions on the confirmation theory. Quine (1970a), for example, solved it by restricting A and B to natural kind terms. My own feeling is that the problem requires a deeper reappraisal of the nature of induction. (Norton, forthcoming a). In the broader reading, the problem of "grue" is just the problem that any pattern can be projected in arbitrarily many ways, with none supposedly distinguished by the earlier history. This broader reading of the problem of "grue" just makes it a version of Humean underdetermination, which I have argued above is distinct from the underdetermination thesis.