No they aren't all culinary.

Those that I know of:
S. officinalis and all of it's cultivars
S. elegans and all of it's cultivars
S. mellisodora -- Grape-scented Sage
S. fruiticosa -- Greek Sage.

(An example of "it's cultivars" would be: Salvia officinalis cv "Berggarten Sage")

I'm sure there are others.

You might want to check out this list of culinary salvias.

In Greece, we boil fresh or dry leaves of wild S.fruticosa and drink it as a tea, use them in meat cooking, and from Salvia pomifera my favourite, we collect the small 'apples' on their leaves (created by some kind of gall wasp infection) and eat them raw when we walk around in the mountains or in salads. :-)