render and redirect_to works in the similar way in your web browser , as they both takes you to a new page but the only difference between them is :

• When you call render it creates a complete response which is sent to your browser.
•  If we do not define a call to our render , it will simply search for the view of the same name as that of your controller's action name.
• You can also render another view in your controller by simply calling the render and providing it with the action name.   eg:render 'profile'
• If you want to render a view to a different controller , you just define the controller name and the action name.   eg:render 'users/profile'
• You can even render the arbitrary files.
• render_to_string is a method which does not send a response to the browser , instead it returns a string which tells what is going to be rendered.

Example:

class UsersController < ApplicationController
    def update
       @user=User.find(params[:id])
       if @user.update(user_params)
         render 'profile'
       end
     end
end

2.1 redirect_to will make a different request to the browser to redirect it to the new location.

2.2 It can take you to a completely different location in your website or to some defined location in your        application.

2.3 By default rails directs you to 302 http request.

Example:

class UsersController < ApplicationController
      def update
         @user=User.find(params[:id])
         if @user.update(user_params)
           redirect_to profile_path
         end
      end
end