Are all cellar spiders the same type?

I think you mean Common cellar spider, see below. if you are referring to Pholcus phalangioides, then yes. But there are many types of spiders found in houses.

The name house spider is a generic term for different spiders commonly found around human dwellings, and may refer to:

Yellow sac spider, Chiracanthium inclusum, a common house spider worldwide.

Black house spider, Badumna Insignis, an Australian spider also found in New Zealand;

Brown house spider, Steatoda grossa, a spider with cosmopolitan distribution;

American house spider, Parasteatoda tepidariorum, a cobweb spider;

Common cellar spider, of the Pholcidae family, also known as daddy long-legs in North America;

Domestic house spider, Tegenaria domestica, also known as barn weaver in North America;

Giant house spider, Eratigena atrica (formerly Tegenaria gigantea);

Hobo spider, Tegenaria agrestis (sometimes called aggressive house spider);

Southern house spider, Kukulcania hibernalis

Tiny house spider, Oonops domesticus

Pholcus phalangioides, known as the longbodied cellar spider or the skull spider due to its cephalothorax looking like a human skull, is a spider of the family Pholcidae. Females have a body length of about 9 mm; males are slightly smaller. Its legs are about 5 or 6 times the length of its body (reaching up to 7 cm of leg span in females). Its habit of living on the ceilings of rooms, caves, garages or cellars gives rise to one of its common names. They are considered beneficial in some parts of the world because they kill and eat other spiders, including species that can be considered a problem to humans such as hobo and redback spiders.