Why do I have two Apple ID/iCloud passwords?

The Apple Account (Apple ID) is the account that logs you Apple device in to iCloud services for file syncing (contacts, calendars, subscriptions, etc) Find My features and App Store purchases. Most users will use a single Apple Account on every Apple device they have to keep interoperation working properly. The Apple Account password can be whatever you wish.

What is an Apple Account? - Apple Support

The Mac User account password is the password that logs you in to your Mac when you restart it. It is the very first thing that you set up when you have a new Mac. The User account password is used only for starting up the Mac and making certain changes to the Mac and system settings like installing updates or deleting software. This password can be set to whatever you like. You can use the same password that you use for your Apple Account, but the two uses remain separate and different - computer user login vs Apple Account login.

If several people use the same Mac, each should have their own Mac User account. That can be addressed in System Settings > Users & Groups.

Mac User Guide - Apple Support

Apple Apple accounts include access to basic iCloud services. You decide which ones to use.

Your Apple Account has but one password. Your passwords will not automatically change to something else. There has to be another explanation.

If you have an account on two computers it will not exactly be the same account. You can set up features which give you access to files on another computer. This alone is a separate question with potentially very long and advanced level solutions depending upon what exactly you wish to do. iCloud syncing is the simplest. Change iCloud settings on Mac - Apple Support If you plan on doing that you may find you need to subscribe to a higher storage level. Read this support article for instructions on how to upgrade to iCloud+ --> Buy iCloud+ or upgrade your current storage plan - Apple Support

If you see different password requests, it may be one context is asking for an Apple Account password and the other is asking for a computer user password. If you have multiple users on your computer, each account likely has its own password. Apple does not say exactly which password you need but you should be able to figure outwhich one by the context. If you are prompted for a password to a user name that is your email address, it is an Apple Account password. If you are signing into your computer account, it wants your computer user password for that account.

Anything to do with an Apple service requires your Apple Account password.

Anything involving changing things on your computer uses your computer user account password.

You could potentially be asked for both in particular situations. I have never been in that situation on this computer (until I started using my current computer I was using an system from 8 years ago). I could see where, for example, if you wanted to change a signed in Apple Account on a computer that it would ask for your computer password to make changes to your computer account information, but then you would have to verify with Apple by using your Apple Account password to prove that you had access to that account. I have not tried doing that so that's just theory.

If you are seeing a prompt that has your full name then it is probably asking for your computer account password. If you are seeing a prompt with your account email address, it is probably wanting your Apple Account password.

When making changes to an Apple Account using a second device, the information should eventually transmit via iCloud to other devices using that account. However, this doesn't always seem to be immediate and it can help restarting devices when you make changes so that the device checks in with iCloud about current settings.

I haven't seen that message but I only have one computer. I also don't know which macOS you are using when you see that, I still use Sequoia.

My interpretation of it is you changed something (maybe an Apple Account password) in your Apple Account using one computer or another device. That change was sent to Apple's main servers and iCloud. Your other computer is now being informed of that change and is asking you if you want to grant it permission to change that Apple Account information on computer 2. As I said, I haven't seen that message but perhaps it's a system app on your computer called "Apple Account" that is trying to perform this information change. Your computer is asking the permission of you as the system administrator on that computer if you will allow it to make the changes it is being received from Apple's main servers and iCloud. It needs your computer administrator password to confirm this permission.

What puzzles me is why it would want you to set a new password again. I would suggest you call Apple and ask what is going on. Refer to this page for Apple Support features ➔ Contact - Official Apple Support

Select from the presented options until you find a solution for your issue, or see if there is a chat or phone call contact method offered lower on the page under “Get more help” (you sometimes have to narrow down the options multiple times before this is shown). If you do not see your issue, keep experimenting with any series of selections until you reach one that offers a chat session or a telephone call and get the representative to redirect you. For chat, you can also try using the Apple Support App —> https://apps.apple.com/app/apple-support/id1130498044

This support article has various country telephone numbers for contacting Apple for support and service ➔ Contact Apple Support - Apple Support For some countries look under “Other” listing at the end of the list. Not every country has telephone support, and phone numbers may only work when calling from the same country.

For chat help with a USA Apple Account —>

https://getsupport.apple.com/?caller=kbase&PGF=PGF63005&category_id=SC0998&symptom_id=20198

1. An Apple Account uses a different password system than the computer; there isn't a rule saying they have to be different, but it's less secure that way.

2. If you're referring to Apple Accounts, it's your choice. If you're referring to computer accounts, that's only possible if you're using the Server application.

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It's just the Apple Account and iCloud is part of it.

iCloud - Official Apple Support

Browse the iCloud User Guide

Learn how to use iCloud.com

I don't use the Passwords feature but I had a look since you were asking about this.

When I open the Passwords application it asks for the password for my name (by which I took it to means the name on the computer account). I enter my computer user password and the app opens.

If I want to set it up through Settings to interface with other devices through Keychain I have to sign into my Apple Account to get access to that feature.

Your Community password is the same as your Apple Account password (anything Apple to do with your account uses the same account information). The 'exception' is if you have things set up the way I do. I have a master password for my browser. Once I enter that it provides user names and passwords for any accounts I use in my browser. So when I sign in here after first starting my browser I use my browser master password, not my computer one or my Apple Account password. As long as I do not close my browser I can sign in and out here as often as I like and I do not have to enter my account information each time.