Technology
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There is a local Administrator account in an AD environment (just like on all Windows systems), but that may be disabled.
As for the domain users, you have a locally created profile and because it caches your credentials you can sign in offline, but your account isn't local in the sense that you could sign in offline (or without access to the domain) indefinitely. For on-prem AD, at least with 2012R2, 2012, and 2008R2 (the last versions I worked with, so can't speak for newer) by default the length that clients held onto that cache was 30 days, but it was configurable in Group Policy. If your device was away from the domain for longer than that you would no longer be able to sign in.
Depending on how your domain is configured you might even have your profile redirected to a network share somewhere, making the account even less local.
Microsoft accounts on personal devices function in basically the same way. If they're offline for too long you stop being able to logon, but you won't lose data in your user folder (unless you've setup profile redirection to One Drive or an SMB share on a NAS).
In neither of those scenarios would I say your account is local, because a network connection is required for initial sign in and then periodically afterwards to be able to use the device with your account.