There are just three main branches of the Stilwell name and these have been well researched.
There are the families descended from the Thursley Stilwells. This is the original branch of the family.
There are families descended from the Dorking Stilwells. These are an offshoot of the Thursley branch and started their dynasty in the early 1500s. All UK Stilwell/Stillwells should be able to trace their line back to one of these two branches.
Then there are the US Stilwells. Almost all US Stilwells can be traced back to a Nicholas Stilwell who settled in Virginia in the 1620s. Who Nicholas was is still a mystery, as can be read on the US Stilwells page.
The double-L spelling of Stillwell is a mis-spelling from the single-L Stilwell and, in the UK, is more common in descendants of the Dorking branch.
Using the drop-down menus under "Key families" above, read about what we know of these branches. In addition there are links to the medical branch of the Stilwells and to the Stillaways.