It matters because ownership decides what you are allowed to do. On a company device you can enforce, wipe and inspect; on a personal one you are negotiating with someone about their own property, and that negotiation needs to have happened in writing before the device holds anything worth protecting.
The common mistake is treating it as a cost saving. The hardware is cheaper and the management is not: personal devices are the ones least likely to be patched, most likely to be shared with family, and hardest to recover when someone leaves. If a client adopts BYOD without a policy covering what may be accessed and what happens at termination, the saving is being paid for with unmanaged risk.