The Short Answer
No, you cannot install an iPadOS IPSW on an iPhone, nor can you install an iOS IPSW on an iPad.
The Technical Explanation
Every Apple device model has a unique hardware identifier, known as a BoardID. When Apple compiles an IPSW file, it is custom-built for that specific BoardID. For example, the IPSW for an iPhone 15 Pro is entirely different from the IPSW for an iPhone 15 Pro Max, even though they were released on the same day.
When you attempt to install an IPSW file using Finder or iTunes, the software performs a pre-flight check. It reads the BoardID of the connected device and compares it to the supported devices listed within the IPSW file's BuildManifest.plist.
If there is a mismatch—such as trying to flash iPadOS onto an iPhone—the installation will immediately fail with an error stating that the firmware is not compatible with the requested device. There is no way to bypass this check, as Apple's Tatsu Signing Server (TSS) will also refuse to generate the required cryptographic signature for the mismatch.
Always ensure you are downloading the exact firmware for your specific device model. See our Ultimate Guide to IPSW Downloads for instructions on finding the correct file.