
Strawberry cordial is a non-alcoholic concentrated strawberry syrup, diluted before serving.
Strawberry syrup is the same role with less fruit character. Fresh strawberries muddled with sugar gives more of the fruit and none of the keeping. Raspberry cordial slots in cleanly and reads as a different drink, not a broken one.
An American cordial
In American usage the word names a sweetened liqueur, alcoholic, poured neat or in a small measure. A recipe using both senses in one line is a recipe worth checking. A recipe from a US source asking for cherry cordial wants a bottle from the liqueur shelf, not a squash.
Strawberry syrup
Sugar and water carrying strawberry, with none of the acid, and it sweetens and does not sharpen, so a drink built on the cordial needs lemon put back.
A sealed commercial bottle keeps for months and wants the fridge once open. Homemade lasts a couple of weeks refrigerated, and the first sign it has turned is a faint fizz, not a smell.