So why is the definite article left out here?
Could it also be: "Vi bor på den samma våning." ?
Samma does not need or use definite forms.
But why doesn't 'floor' use a definite form here? Would this be constructed differently if it said something like "we live on the third floor"?
Yes, in that case it'd be "tredje våningen". The adjectice samma can't be used with a definite noun.
Ah, I see. Thanks for the clarification :)
No, it would actually be "fjärde våningen"! Floors are counted different in Sweden: "första våningen" is "ground floor", "andra våningen" is "first floor", and so on.
Sadly, both a system with ground floor, then first, then second and a system with first (ground), then second, then third etc. are used.
Couldn't you also say Vi bor på samma golvet?
No, for two reasons:
i samma våning = in the same apartment?
No, i samma våning just doesn't make sense. Technically, the våning refers to 2D so "in" doesn't work.
Yes, that's correct.