Are "monoliths" giant, isolated rocks sitting in dirt, or are they continuous with bedrock I am at a loss for the precise, correct terminology, but I have read in Wikipedia that Uluru is not a monolith, but Savandurga is, and that I probably shouldn't be using the word monolith to begin with, but instead use inselberg.

I was once told that Uluru is a giant rock, just sitting in the soil. I think this is probably impossible and that it is part of the underlying bedrock of the area, but is that the case for all/most inselbergs? Are they identified primarily by how isolated they appear above ground only?



below: Savandurga (India) from here. See more photos at Savandurga - A Hill composed entirely of only one rock.



below: Uluru (Australia) from here.
the trick is not all isolated rocks are produced the same ways. Of the two in your pictures  the first is an old volcanic events; intrusions, dikes, ect. depending on which rock in the region you are talking about. The whole deccan plateau region is full of them, some have been exposed on the surface via erosion. Basically everything else eroded faster than they did leaving them sticking out. 


The second was produced by the same effect (eroding slower than the rock around it) but this time it was just a hard massive sandstone formation surrounded by more easily eroded rock. It is part of the bedrock.