Actually it's the same ad hoc testing just renamed to "exploratory" to free oneself from synonymous with sloppy and careless work and to allow beginning development of the practice into a teachable discipline.

Nowadays more and more clients ask me about benefits of ET if compared with more traditional - scripting testing. I recommend it when:

• there is poor documentation of the product
• there is not enough time to organize classic scripted testing
• the testing of product was never conducted
• there is very limited budget on independent testing

By the way I keep the notion that Exploratory and Scripting testing go well together and supplement each other through the product testing life cycle:

• Exploratory testing will lead your team to the scripted process one day or other if you keep testing for the same product for a long time;
• Scripted testing is always supported with exploring which allows us to do the better tests every time. IMHO it's the one way to prevent minefield effect.

Exploring the software testers feel free in their actions and use their experience as well as they can. That is way the more the tester knows about the product and different test methods, the better the testing will be. From the other hand the approach makes testers' work interesting and gives good opportunity and motive to improve themselves.