Thanks for reaching out to the Community for help. I'll shed some light on the key differences between QuickBooks Online and QuickBooks Self-Employed.
QuickBooks Self-Employed doesn't have the ability to integrate with third-party applications, and can't be integrated with TSheets. The Self-Employed platform is also designed for an independent person that runs a business without any employees. TSheets is designed to help you streamline employee hours.
If you're looking to utilize the TSheets app, I recommend staying with QuickBooks Online. This platform has the ability to sync with tons of different third-party apps.
I hope this helps. If you have any other questions, just let me know.
Have a good day.