The Alkaline PP3 do have 6 x AAAA, or close enough to save money if you need AAAA cells. Zinc Carbon PP3 are always Layer and Alkaline PP3 are always cylinder (can be almost identical, some packs use slightly shorter cells).
This is why Alkaline is 590mAH and Zinc Carbon about 460mAH at low current. The Alkaline cells don't fill the case so well. Compare Zinc Carbon AA at 950mAH to 1100mAH and Alkaline AA about 2500mAH to 2700mAH at low current. This why 90V HT using layer cells adopted rather than using 60 x B cells. PP9 Zinc Carbon layer cells about 5,000mAH.
The older NiCd used 6 x rounded rectangle "button" like stacked cells a little like the 3 on 3.6V PCB backup battery.
6 x NiMH cells is slightly more volts than NiCd, so is thus about 7.4 to 7.5 nominal rather than 7.2, those may on occasion be AAAA. But there are 7 cell and allegedly even 8 cell NiMH. These probably use stacked cells like the NiCd version but thinner.
Layer cells in the sense that Zinc Carbon exist isn't possible with Alkaline, NiCd or NiMH. On Alkaline the top cap is part of the outer cylinder (+ve) unlike ZnC cylinder where the case is the Zinc negative electrode and positive is carbon.
I have never seen an explanation of how the Zinc Carbon Layer cells work. They don't have metallic zinc. The negative must just be Zinc Chloride. The Carbon rod (or surface in a layer cell) isn't really an electrode. It's just any common metal would dissolve in the Manganese Dioxide paste. It's possible the layer cell is a part way development toward the Alkaline cell.
It's more than a little confusing that Alkaline, Zinc Chloride and Zinc Carbon have similar chemicals and all rely on Zinc and Manganese Dioxide to generate the voltage.