Pumpkins are a variety of squash ... which originated in the Western hemisphere ... in the US canned pumpkin will be either the smaller pie pumpkins or more than likely the larger field pumpkins. In Australia butternut squash is also known as "butternut pumpkin" - which is in line with what bethzaring said.
Perhaps the largest producer of canned pumpkin in the US is Libby - they produce two varieties ... 100% Pumpkin (which is just that, pure pumpkin puree) and Pumpkin Pie Mix (a mix of pureeed pumpkin, sugar, and spices).
What "thickens" canned pumpkin is the processing. It's basically this: the pumpkin is cubed, steamed, pressed thru a sieve (to remove fiberous material and seeds) then pureed, then "pressed" to expell excess moisture, maybe a 2nd cooking to remove more moisture, and then canned and processed.
Using fresh pumpkin- the more moisture you remove the thicker it will be.