Are these the same? What does the route keyword accomplish here?

Here it accomplishes nothing. But you could do:

app.route('/some/very/long/path/that/you/dont/want/to/duplicate/risking/errors')
  .get(function (req, res) {
  })
  .post(function (req, res) {
  })
  .put(function (req, res) {
  });

Instead of:

  router.get('/some/very/long/path/that/you/dont/want/to/duplicate/risking/errors', function (req, res) {
  })
  router.post('/some/very/long/path/that/you/dont/want/to/dpulicate/risking/errors', function (req, res) {
  })
  router.put('/some/very/long/path/that/you/dont/want/to/dulpicate/risking/errors', function (req, res) {
  });

router.route(path) creates an instance of a single Route for the given path.

Using router.route(path) is a recommended approach to avoiding duplicate route naming and thus typo errors.

router.[method] like "post" and "get" These are functions which you can directly call on a route to register a new handler for the method on the route.