No, they’re all independent plugins, currently with different approaches that may work better in certain scenarios. There’s a bit about it on the forum, but will announce/do some videos to show the differences.
Which one should I use today? For most general users, I’d say Static HTML Output 6.6.21 gives best results for lowest learning curve.
New WP2Static has quite a few users, but currently leans more towards more advanced/scripted workflows.
SimplerStatic is just an updated version of SimplerStatic at the moment, but that in itself, has benefits for some low resource hosting environments if the other 2 don’t work.