Most users have a OEM version provided by a big brands like Dell, Asus, HP, etc. that puts the key in BIOS/UEFI or those that accepted the Microsoft offer to upgrade from Windows 7/Windows 8.x have the key stored on the Microsoft activation servers.
True. To be 100% correct in my prior statement, "It is not necessary to have a product key to install the same Edition (e.g., Home, Pro) of Windows 10 on any machine that had it legally installed and activated on it in the past, regardless of whether the machine originally came with Windows 10 or not."
The only time one needs a product key on a Windows 10 reinstall is in one of two circumstances:
1. You have replaced your motherboard and, for some odd reason, could not or did not want to contact Microsoft about doing a free reinstall using the procedure for a change in motherboard.
2. You are upgrading your Edition of Windows 10, e.g., your machine came with Home and you now want to install Pro or Enterprise. Technically, you don't even have to do a reinstall to make this happen. If you go to Settings, System, About Pane you will find a link, near the bottom, that reads, "Change product key or update your Edition of Windows." If you activate it you will be prompted to enter the new product key and, based on what Edition that key is for, the features for that Edition will be activated. All Editions of Windows 10 carry all of the features for all Editions along with them, the product key is what determines which are active and visible to the user.
Brian AKA Bri the Tech Guy (website in my user profile) - Windows 10 Home, 64-Bit, Version 1803, Build 17134
. . . the presumption of innocence, while essential in the legal realm, does not mean the elimination of common sense outside it. The willing suspension of disbelief has its limits, or should.
~ Ruth Marcus, November 10, 2017, in Washington Post article, Bannon is right: It’s no coincidence The Post broke the Moore story