If you are in a role with publishing permission, you can publish a page or asset (for certain assets) directly without first approving it. This automatically approves and publishes the item for you. If a user is not in a role with publishing permission, they only have the option to approve, after which the next process would be for an admin to publish.
If you don’t want it to be published yet, click Approve on the right. But if it is something you are reviewing to get live right away, instead of Approving and then Edit > Publish, just do as you said, and Edit, then Publish.