No, they are not the same.
I want to reset my Windows 10 Mobile back to 8.1
In your case Windows Device Recovery tool is the only option. Here is the reason.
- Hard reset will not change the version of Operating system. The OS and firmware version remains the same.
- Only files, apps, settings and other data will be lost.
- In your case, the phone will remain in Windows 10 Mobile.
- It does not require any internet connectivity.
Windows Device Recovery Tool
- Windows Device Recovery tool on the other hand will install the latest version of Windows 10/WP8.1 (WP 8.1 for your phone).
- This tools also installs the latest version of firmware if available.
- It requires Internet connectivity.