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.