PCIe Half Mini Card and M.2 (NGFF) are in fact different board form factors. They use different connectors and each type of card requires a compatible slot in the system board.
If your PC has a PCIe HMC slot, the M.2 board will not fit in.
The Picture above shows a PCIe Half Mini Card and a M.2 (NGFF) board for comparison.
Even if both adapters used the same Form Factor, we would advise you to contact the manufacturer of your PC so they can let you know which Intel® Wireless adapters can be used in your computer.
Intel Wireless Adapters can only be installed by the manufacturer or its authorized representative.
Before a determined wireless adapter is used in a computer, it must comply with specific regulations, and other compatibility requirements. If these requirements are not met, the adapter may not operate correctly, or may not work at all; in some cases, installing these adapters in an unauthorized system may be illegal.