Windows 10 only uses a key if you bought the full package (retail version). If you upgraded then it uses Digital Entitlement. Retail full package come with 32 and 64 bit which use the same key. OEM Windows 32 bit and 64 bit are different product and wouldn't have the same key. Going from 32 to 64 bit can't be upgraded and requires a new install.
Weirdly, this is not always a reliable rule. I know, odd, but it isn't. For example, I have a retail copy of W10Pro that I upgraded from my retail copy of W8.1pro (which was an upgrade to W7 which was retail) so I have a retail licence and can transfer this version between builds (as I have done). That is registere4d with a digital entitlement.
I also have a Stick PC that came with W10 pre-installed, so an OEM version. This cannot be transferred between PCs of course. Interestingly, it is registered with a key and not a digital entitlement.
So, there appears to be no firm rule as to what type of Windows licence you will get. A retail copy can be digital entitlement, and an OEM copy linked to a PC can be key code. The only thing you can be sure of is that a retail copy is transferable between devices and an OEM copy (pre-installed or from OEM discs) is not so transferable, even if you buy an upgrade to pro or some such. Full retail, or you're stuck.
This is why it is rarely useful to upgrade an OEM copy of Win Home to Pro. Better to buy full Win Pro retail box so you can transfer it to your next PC. Larger initial outlay, but saves money as it doesn't die with your old laptop.