The term "unlock" is confusing, as it can mean several different things.
Since a SIM works from a carrier besides where it was purchased from, it appears the phone is not SIM-locked. But that has nothing to do with S-Off and root, which is what you need for flashing ROMs, kernels, or any mods/apps that require root.
If I recall correctly, some of the European Z's are sold unbranded, and possibly not SIM-locked. But as far as I know, you will never get a phone from your carrier that is S-Off and rooted. Follow the Wiki method to get S-Off and root. And if you do so, it doesn't matter whether its SIM-locked or not, as it will be SIM-unlocked after the S-Off and root process (gfree does S-Off, root, Super CID, and SIM unlock).
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Phone: HTC One X (AT&T version) Rooted, Bootloader Unlocked, S-Off
Tablet: Samsung Galaxy Note 8 (WiFi only) Rooted