In InfoPath, a save is typically the same as a submit: both save the form to SharePoint. The typical pattern is to add a "status" field to the form. Give it a default value of something like "saved". Then, add two buttons to the form. One will submit the form as-is, so the status field will still be "saved". For the other button, add an additional action to set the status field to "submitted", and then submit the form to sharepoint. For the approval, create a SharePoint designer workflow, which has an approval action (in the "2010" workflow engine, which is still available in newer versions of SharePoint)
The first step of the workflow will be to check the value of the status field: if it's saved, end the workflow. If it's "submitted", then go on to the next step and start the approval.
btw, I mention SharePoint designer because you mentioned infopath. Both tools are older at this point. If you're in SharePoint online, certainly do the above with PowerApps and Flow.