Firstly, you stated you have a laptop, but didn't specify how old the laptop is (which makes a big difference) nor stating your copy of Windows came from anyplace else than the laptop maker (key or not).
Given that all devices (except self built) are sold with a OEM Edition of Windows right off, the 'key' since Windows 7 was released was first embedded in a LOCKED BIOS by many manufacturers, then when W8 release was integrated into a unaccessible part of UEFI (which replaced BIOS). With Windows 8 if you 'installed' Windows initially from ANY source (didn't matter) and ANY edition, it would read the UEFI key and only enable the editions to your specific hardware (so you bought Ultimate edition it would only setup "Home" edition). This was initially to make it easier on OEMs to just issue a generic OEM Windows (really a full edition of W8) and then leave it to the 'hardware' to 'sort things out'. Problem was this initially effected STORE (Walmart, Amazon) bought editions.
The fix eliminated this 'problem' but still would look for OEM editions to do the same thing, but any Store bought would get a 'different key' and would 'error' sometimes when doing reloads / restores of the system.
Windows 10 takes the whole thing and puts it on Microsoft's Servers. When a edition of Windows wishes to 'start up' it has to check with Microsoft on how 'legit' it is (and of course all the patches and fixes they push like your cellphone does when you turn it on). When Windows 'first' installs it take the EXACT hardware inventory (so it knows how to talk to the keyboard as compared to your wifi) and REGISTERS it with the Windows Key (either from the UEFI or from your 'Store bought' manual input when prompted) and FOREVER will say "This KEY is ONLY for THAT hardware ONLY", if I see it anyplace else BOOM - Flagged and reported as Pirated to Microsoft and on your PC, then attempts to block you from using it in various 'internal' ways. In the case of OEM editions, the UEFI goes a step further and BLOCKS Windows from loading /repairing / etc. in somecases if a 'OEM" edition other than the legit one (trying to use HP OEM on a Dell for example), and so on.
Long Story short (as we have alot of parameters that effect the outcome as I demonstrated) you have a laptop, laptop has the key 'built in', any legit copy of Windows from the OEM will work on that laptop based on the key (as I said can't 'cross' OEM) and will be 'fast easy reinstall'. If you take the drive / Windows to another PC, Windows will refuse to load / repair/ reinstall etc. because it is OEM (why you got a "different key") even if you tried to input another key.
You HAVE to know where that edition of Windows came from. You HAVE to know where the key came from. There is no 'Tutorial' edition of Windows Keys and highly suspect you have a 'hacked' one (aka pirated). While there WAS a old program from Microsoft that has long been expired (I know because many of my keys I legitimately used under it were 'expired' on me) for those Developer Editions, used solely for testing boxes and the like, and now is done in a totally different way.
So all depends on the copy of Windows you have, where the key came from etc.
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