It is possible to transfer the operating system to a different drive. It is necessary to use cloning software. Intel; Kingston, Crucial and many other Solid State Drive manufacturers provide with the software (included with the SSD).
In regards the Intel® NUC Kit 5PGYH, it comes with an embedded eMMC drive of 32GB and it is possible to include a regular 2.5” drive (laptop form factor). It could be a Solid State Drive or regular Hard Disk Drive.
Intel® Solid State Drives available:
The M.2 slot with PCIe X1 lane is already occupied by the Bluetooth-wireless card.