Hi swell1018,
Your iCloud password will be the same as your Apple ID password, so the behavior you describe when attempting to reset that is expected.
A possible reason you may not be able to sign into iCloud on your Mac would be if you have enabled Advanced Data Protection for your iCloud account. How to turn on Advanced Data Protection for iCloud describes this feature in greater detail including a list of requirements:
"To turn on Advanced Data Protection for iCloud, you need:
- An Apple ID with two-factor authentication.
- A passcode or password set for your device.
- At least one account recovery contact or recovery key. If you don't already have one, you'll be guided to set one up when you turn on Advanced Data Protection.
- Updated software on all of the devices where you're signed in with your Apple ID:
- iPhone with iOS 16.2 or later
- iPad with iPadOS 16.2 or later
- Mac with macOS 13.1 or later
- Apple Watch with watchOS 9.2 or later
- Apple TV with tvOS 16.2 or later
- HomePod with software version 16.0 or later
- Windows computer with iCloud for Windows 14.1 or later"
As your Mac presently has macOS 10.10 installed and you indicate it cannot be upgraded further, it does not meet the requirement for that security measure. From that same article:
"While Advanced Data Protection is enabled for your account, you can sign in with your Apple ID only on devices that meet the software requirements listed above."
That article also includes a section for disabling that feature which would be necessary to sign in on any device not able of meeting the requirements as listed above.
Regards.