A good question....
Which do we use for aquariums and why? What is the difference?
To keep it simple, they are manufactured differently.
Extruded Acrylic is made using an extrusion/die method. This way is the cheapest way to make an acrylic sheet.
This is a fast, horizontal production of extruding acrylic.
How extruded acrylic is made is by doing the following:
Resin pellets are fed into an extruder. Which heats them until they turn into a molten liquid.
This liquid is then forced through a die which forms a molten sheet. It then air cools, and is done. VERY fast, very cheap to do.
Cell cast is made by one of three ways...
The first way is by liquid cooling. Acrylic syrup is poured into a mold made from two tempered glass sheets. The syrup is poured into to this mold, and how ever far apart those two sheets are, is how thick the acrylic will be. The mold is then submerged in a cool liquid, which maintains the proper temperature for the acrylic to cure properly. This makes sure the acrylic does not cure too quickly.
The second way is the same as the first, but instead of cooling it in liquid, it is cooled in an oven that blows hot air over the mold, which gets cooler and cooler with time. This also stops it from cooling too quickly.
The third way is also the same as the first... but or the cooling process, the mold has special chambers filled with water that cool the acrylic slowly.
All cell cast is made the same, except the way it is cooled changes.
So the differences here are the way they are cooled, and the starting material for each. Cell cast acrylic is already a syrup before it hits the mold. so it is already bound at a molecular level. Extruded is not.
The end result...
Cell cast is the harder acrylic, with far better physical and optical properties than that of extruded.
Extruded is a "soft" acrylic, and is limited in the sizes it can come in.
ALL aquariums need to be made from cell cast. Extruded is too soft. Although small sumps, and small tanks up to about 10" tall, and not very long, is fine with extruded from my experience.