Ideally, there should not be any difference, and the sidebar and navbars paths should be determined in the same way no matter the routerMode.
With hash router mode, it seems that the paths are determined from the base of the site, whereas with history router mode, the paths are determined based on the current page path.
PR https://github.com/docsifyjs/docsify/pull/1970 adds more documentation on how routerMode currently affects sidebar and navbar loading.
Ideally, there should not be any difference, and the sidebar and navbars paths should be determined in the same way no matter the routerMode.
With hash router mode, it seems that the paths are determined from the base of the site, whereas with history router mode, the paths are determined based on the current page path.