Have you logged in to your Microsoft Account, on the Microsoft Website, using a specific password? If so, this is your Microsoft Account password.
It sounds like you have logged in to your 64-bit machine using a Windows 10 account that's linked to your Microsoft account, and that probably shares the same e-mail address and password. That e-mail address and password are specific to Windows 10 on that machine. If you changed your Windows 10 password it would not change your Microsoft Account password (and vice versa).
It's clear that your Windows account password on the 32-bit machine does not match that on your 64-bit machine nor on your Microsoft Account. If you did not set up a password hint that helps you to remember what you used, or create a password reset disc/USB for the machine that's giving you issues before the fact, you are likely stuck.
I would suggest taking a look at this article at HowToGeek on resetting your password and/or working around the inability to do so.
Brian AKA Bri the Tech Guy (website in my user profile) - Windows 10 Home, 64-Bit, Version 1803, Build 17134
Memory is a crazy woman that hoards rags and throws away food.
~ Austin O'Malley