I agree with GalacticCowboy's answer that there's a good deal of overlap between the approaches—especially when it comes to observation and interpretation. Roughly speaking the difference amounts to nothing more than who is doing the work.
I'm not sure if other traditions have anything quite like inductive Bible study, so the rest of this answer is informed by my own Protestant background.
A good inductive study will level the playing field between participants since the foundation of the method starts with observations of the text itself. Interpretation springs from the observations rather than doctrine or outside knowledge. Ideally, all participants will have equal access to resources such as cross references, concordances, Bible dictionaries (for historical background), interlinear Bibles, and so on. The studies I've been involved in do not allow commentaries or evidence that shortcuts the interpretive processes. So if you've spent years listening to sermons, you still have to do the work of discovering meaning in the text as if you've never had any interaction with the Biblical texts at all. (In theory, of course. In practice, "chruched" people get lazy and turn off their brains without some prodding. Human nature, I guess.)
Hermeneutics is the set of tools scholars use to produce commentaries. In some ways the rules of the game are more strict and less accessible since commentators are expected to know and interact with other commentaries. But if you spend time reading commentaries, you'll find that often their notes don't strictly adhere to the text under examination. To take an example more or less at random, John MacArthur, an expository giant if ever their was one, takes time out of a sermon on Ephesians 5:18 ("And do not get drunk with wine, for that is debauchery, but be filled with the Spirit," ESV) to talk about Timothy Leary. (Not that I think MacArthur went off track in the sermon, but that not everything you read in a commentary follows the rules of biblical hermeneutics.)
In addition, Biblical commentators tend to work alone, which inductive studies usually occur groups. As such, published commentaries are more likely to have interpretations that are novel and Bible studies search for consensus.
These approaches most strongly overlap when they directly engage with the text at hand. Those of us who participate in inductive studies would do well to borrow methods, tools and techniques from our professional brothers and sisters. Recently, for instance, popular works by Bart D. Ehrman (notably Misquoting Jesus: The Story Behind
Who Changed the Bible and Why) have led our study to occasionally engage in textual criticism. Thanks in part to books like C. S. Lewis' The Four Loves, we go back to the original languages to try and understand our text's nuance. Similarly, N. T. Wright's exceptional work in the milieu of the first century has spurred me to consider interpretations better grounded in the Bible's historical context. John Piper has been a strong influence, not just for his tightly reasoned approach to exegesis, but also his tireless drive to follow the text where ever it may lead.
Following the examples of these men (and I'd be remiss to not mention Kay Arthur and Beth Moore), a good inductive Bible study encourages the participants to dig deep and not rest on the casual interpretation so many Christians are content with. Like all scholars, individuals are expected to think about the texts and form opinions. Differences in opinion are resolved by the application of reason in the from of debates. Over time, the best solutions to interpretive problems become the answers accepted by consensus. Even so, new evidence can always lead to radical reinterpretations if required.
In the end, the goal of both methods is the same: producing clear understanding of sometimes difficult, ancient documents.