they are not the same.
in the first case you define two different express apps, which can have their own set of settings, templates (and engine), middleware and routes. 'app' mounts 'one' as sub-app, but 'one' could be used as the main app itself.
the second case you have only one app, and you have defined a set of routes on one router. in express 4, the Router is visible and can be instantiated several times, i.E. to bundle routes in an app logically. but they do not have separated settings, they are plugged in the same middleware chain. so in your second example you did nothing else than to define one single route: 'GET /one/'
the first approach is usefull when your web application is highly modular and got assembled at configuration time. Every sub-app can be developed as stand-alon app, with its oun templating and routing and even own middlewares, and be even deployed as dependency via npm. the second approach is the defaul wy to defin routes in express 4 and you can use several Router instances to group routes logicaly, i.E. per resource or per access restrictions. it makes it easier to define middlewares specific to a group of routes this way.