What players call those, doesn’t matter.
By definition and design, the old talent-system was not structured to act as dedicated core specializations. You can call what we had back then Specializations all you want. It does not make them so.
Here you got the WoW manual itself specifically saying that each class had 3 different types of “Talent Categories” with talents being sorted based on the class main strengths.
Every class has three categories of talents that are organized by
your class abilities. Mages, for instance, rely primarily on their
spells, which are broken up into the arcane, frost, and fire schools.
Thus, the mage’s talent categories are arcane, frost, and fire. Each
category can be accessed using the tabs at the bottom of the
Talents window.
You can find that here, on page 90:
http://us.media.blizzard.com/manuals/wow/wow-classic-manual-enUS.pdf
Furthermore:
The talent system is tiered. There are low-level talents you must
buy and master before you can learn high-level talents. However,
you can see all talents in a category, and see the paths leading to
all talents
All classes have talents that allow the player to customize their character.
Talents can be applied in the following ways:
-To improve a class’ existing spells or abilities.
-To alter the functionality of existing class spells or abilities.
-To acquire new spells and abilities.
-To improve class skills.
The three lines of class talents are geared towards each class’ main
strengths. For example, mages naturally divide their talents into arcane,
frost, and fire, which mimic the three main schools of magic mages learn.
Nowhere in that entire section are Talents/Talent Trees referred to as being Specializations.
And this matters here why?
Meaning?
Not even close.
As the Manual states, talents back then only served to enhance, slightly alter, or add to the existing toolkit.
There’s nothing even remotely the same as what we have today with specializations that completely remakes what your gameplay is like, depending on which one you pick.