>you can't go round patenting things which already exist

Not strictly right but close enough, better (but still not the whole story due to US differences) would be "things which have already been made public".

Prior art is the globally recognised term. It means any [relevant] disclosure prior to the priority date of the application in hand.

As an ex-patent examiner (not US) I'd use "background art" to represent the general status of the field (often presented in the preamble of the specification) and "state of the art" is strictly the whole gamut of prior art disclosures.

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most jurisdictions have first to file whilst US has a "first to invent" system