Azure backup vs Snapshots

I read that Azure backup takes snapshots and then uploads them to the vault.

You are right, Azure backup will take snapshots first, then upload them to backup vault.

how using 'Azure backup' to backup a VM is different from taking the snapshots of OS Disk and data disk of azure VM via "az vm" cli commands?

The biggest difference is that, we can use Azure Backup to restore VM directly. If we use snapshot and want to restore VM, we have to use snapshot to create OSdisk and then use this OSdisk to create new VM.

By the way, we can set backup jobs in Azure Backup, so Azure can run backup by backup policy. If we use snapshot, we should do it manually.

What exactly is the vault here?

The vault same as storage account, but we can't find it in our portal, and can't migrate backup data, we can manage the vault via Azure Backup.

Which is better cost wise, azure backup or osdisk snapshots?

For now, we can use CLI 2.0 command az snapshot create to create snapshot, but we can't use this to snapshot some on-prem resource.

If we just want on-time backup of Azure VM, and we can use PowerShell to restore it, I guess we can use snapshot.

If we want to daily backup of VM, I think we should use Azure Backup.

About cost, Azure backup and snapshot charge for the usage of storage account.

using azure backup or taking a snapshot of OS disk/Data disks. Is there an advantage of using one over the other?

In my opinion, take snapshot used for restore VM to one time, for example, I want to do some configure change, before that I take a snapshot of it, then change the configure, if it false I can restore VM with the snapshot.

Are the Snapshots of OS disk taken in Azure, global in nature or are they in any way associated with a region? If a region is down, do they become unavailable?

we can choose SKU for snapshot, Premium_LRS, Standard_LRS. so you are right, if the region is down, the snapshot will unavailable.

In the azure portal, snapshots, what is "snapshot state"? Why is the snapshot state "Unattached" for me even after spinning off a VM from the snapshot disk?

We can't attach the snapshot to Azure VM, so the state is unattached. I have create a disk from the snapshot, and the state is unattached.