You're misremembering slightly.
"Tank", in MMOs of that era was a verb and a noun. In pre-TBC WoW, it was not a "role", it just something you did, and class could do it - and Warlocks and Rogues and other classes often ended up doing it. "Tanking" was the act of standing in front of the party and trying to hold aggro on the mobs. In non-WoW MMOs, often multiple classes could do this, and had tools to do this. In DAoC, for example, it was role, and a bunch of classes had it, and a bunch of other classes were hybrids that could do it, or could do other things.
In WoW pre-TBC only one class was actually a Tank by design - the Warrior.
That was it. That was the end of the story. You didn't be a "Protection Warrior" to Tank in WoW. All Warriors, regardless of how they spec'd, had the tools to Tank and go a good job of it. In fact, in that era, Warriors didn't spec Protection to tank unless they were the Main Tank in a Raid (which only one player in 40 could be, even theoretically). It was actually counterproductive in dungeons - Fury, hilariously, made the best tank there. That remained true even in TBC (because killing mobs faster and holding aggro better > taking slightly less damage).
What was notable about WoW, and not like other MMOs, was that the other classes didn't have the tools they needed to Tank (Druid was closest, with Bear form). In other MMOs, you usually had several classes which could tank decently to excellently. In WoW, just Warriors. Again, this was something people were mad about.
This changed, on paper at least, in TBC. They added tools to Paladins, they improved the tools Druids had. In theory you could now tank okay as those classes. In practice it was more debatable, until very late in TBC, when well-geared Paladins became the best tanks for dungeons. It was still informal, though. The first formalization of it was in WotLK, when the LFG tool asked you to identify your role (that wasn't on launch of WotLK, though, so 2009 some time?). Cataclysm then formalized it more, by actually creating separate "specs" with exclusive abilities.