Every login in your screenshots is the user ENALOG\Peter, not NEMOQ_AD\Peter. It doesn't matter that you're typing the domain NEMOQ_AD\Peter, since NEMOQ_AD is not a domain that ENALOG trusts. Notice that you don't see "NAMOQ_AD" anywhere once you've connected to Voldemort.
NTLM supports something called pass-through authentication. The important bit of the article is here:
If the domain name specified is not trusted by the domain, the authentication request is processed on the computer being connected to as if the domain name specified were that domain name. NetLogon does not differentiate between a nonexistent domain, an untrusted domain, and an incorrectly typed domain name.
What is happening is the following:
- Voldemort receives a request to authenticate the user NEMOQ_AD\Peter.
- Voldemort sees that NEMOQ_AD is neither its own domain nor any domain that it trusts.
- Voldemort tries to authenticate the user ENALOG\Peter instead.
- Since you entered the password for ENALOG\Peter (as you said in another comment), authentication succeeds.
When you are accessing the drive share, you have to be using NTLM (any attempt to use Kerberos will fail because ENALOG doesn't trust NAMOQ_AD) using pass-through authentication, which allows you to access network shares without typing a password. This works only when you are using identically-named accounts with an identical passwords on the two machines.
When you enter a password when using Remote Desktop, it's behaving exactly as if you had tried to log in as ENALOG\Peter instead of NEMOQ_AD\Peter, and using whatever password you typed in. This way, if you type "Peter" as your username, the local computer sends "NEMOQ_AD\Peter" since that's the only domain it knows about, but the remote computer decides to try "ENALOG\Peter" instead.
I assume SQL Server Management Studio is using one strategy or the other (probably the second one), I don't know exact details of its implementation and don't have two domains lying around to test it.