Hi,
There is quite a misunderstanding in your question.
Project Online is a Project Management solution which proposes a web client AND a desktop client. The desktop client (MS Project) can be connected to Project Online in order to update, save and publish to Project Online the project plans. The project plans can also be edited through the web interface (Project Web Access) of Project Online.
- Your first screenshot, the tutorial, shows the desktop client: MS Project Professional 2013 (or 2016).
- Your second screenshot is your project schedule opened in the PWA, the web interface.
You can either go on working on the schedule in the web interface, or purchase MS Project Pro for O365 to connect it to Project Online.
https://products.office.com/en-us/project/project-pro-for-office-365