
Chocolate syrup is a pourable cocoa-flavored syrup. There is no dairy in it at all: it is cocoa and sugar in water, thickened only by a gum, which is why it stays thin.
Cocoa powder in sugar syrup covers the same ground, provided you dissolve it warm; in cold liquid the powder clumps and settles. Crème de cacao brings chocolate with alcohol and its own sugar attached, so both need accounting for before it stands in.
Chocolate sauce
Chocolate syrup is a thin, pourable, all but fat-free mix of cocoa and sugar. Chocolate sauce is richer and thicker, usually made with melted chocolate or dairy fat such as cream and butter. The words get mixed up, but the products differ in fat, density and flow — the sauce will not disperse in a cold drink and sinks instead.
Chocolate cordial
Acid added to the same chocolate, usually in-house. It sweetens and sharpens together, so the drink wants less citrus in its place.
A commercial bottle is stable for months and belongs in the fridge once opened. A homemade one is cocoa, sugar and water, preserved only by its own sugar and not very strongly — the cocoa solids give bacteria more to work with than a plain syrup does. A fortnight chilled, and the cocoa settles out as it stands, so shake it before measuring.