Anyway, the reason is that s370 (which is short for Socket 370) has had a decently long run and featured at least 3 different generations of CPUs (Mendocino, then Coppermine and lastly Tualatin).
The very first Celeron was basically a Pentium II with its off-die cache completely removed. This was the Covington. However, Covington performed a bit lackluster to say the least so Intel then basically made an emergency edit to the Covington and added 128kb of on-die cache to it. This was the Mendocino.
While Covington was available in Slot 1 format only (for desktops anyway, dunno from top of my head if there were any laptop versions of that), Mendocino first appeared in Slot 1 format as well (it included the somewhat legendary 300A), but later Intel decided to create an entirely separate platform just for Celeron, creating Socket 370 where Slot 1 was to remain as the top-of-the-line platform.
However, manufacturers then started to create adapters so people could still use the s370 Mendocinos in their Slot 1 systems.
These Celerons ran at around 2v or a bit less.
Later Intel created the Coppermine core, which was basically (again very basically) a Pentium II/Pentium III Katmai core with its outer off-die cache completely removed, but with 256kb cache on-die added. This core also received a dieshrink, lowering voltage to around 1.6v (going up to 1.75v or so for later models).
This new CPU also got a Celeron version with half the cache amount, also coming with 128kb (same as Mendocino).
However, these Coppermine Celerons were not always compatible with the SLotkets that had been manufactured up to this point.
That is why it is important to figure out which slotket to get for which CPU.
Things became even a bit more complicated once the Tualatin Celeron (also dubbed the Tualeron, which is not an official Intel name but is well known name amongst retro computer hobbyists) arrived on the market. These featured a lower voltage again, 256kb cache instead of the 128kb the Coppermine Celerons had.
The Pentium III Tualatin and Tualeron were basically divided by Tualeron being set for 100MHz FSB and the Pentium III for 133MHz FSB.
A second version of the Pentium III Talatin got 512kb cache, ran at 133MHz FSB as well and this is the Pentium III-S or Tualatin-S.
The Tualatin cored Pentium III got the same name as the Coppermine cored Pentium III, hence it is easier to distinguish them from another by naming the Tualatin cored Pentium III the Tualatin.
All Tualatins ran at around 1.4v to 1.45v or so.
The relevant cores for lowend - highend were something like this (and this excludes laptop and server parts).
Mendocino - Deschutes/Katmai (±2v)
Celeron Coppermine - Coppermine (±1.6v to 1.75v)
Tualeron - Tualatin/Tualatin-S (±1.4v to 1.45v)
with the bolded parts being the 3 different generations of Celerons that were available for s370
Hope this explains it a bit better. It can be quite confusing, if only because at times manufacturers made it confusing on purpose, so sometimes terms like "Tualeron" are simply better and often more accurate, thus reducing both potential and guaranteed confusion.
