Is there a common word for floor and ceiling?

Believe it or not, the word you are looking for is floor.

It refers to both the space between and the actual divisions. But the space between can have other names like story ("storey" in British English).

If it were a house it would be the roof.

I think you could use "floor slab" or deck.

The actual word for a vertical partition between two stories is called a Party Structure.

Wanted to create a different answer because my other answer was related but different.

• NOTE: This word is used more in the UK than it is in the US.

Party Structure Diagram

You could use the word Partition. It is even more general and doesn't specify vertically or horizontally. It defines an object which separates something into parts.

So: For a building, a partition separates the building into floors, stories, rooms, or whatever your preference is. As TheFreeDictionary.com says,

partition: a division into parts; separation

A common English term is stories:

"This building is seven stories tall."

EDIT#1

and alternative is floor:

"All the bedrooms are on the fourth floor."

See 3-A