
Cane syrup is a sweetener made by evaporating pressed sugarcane juice into a thick syrup without crystallizing out any of the sugar.
Thick and coating on the palate, with a full sweetness carried by a mild whole-cane-juice aroma.
Bartenders stir it into the build or pre-dilute it before shaking, since its viscosity makes it disperse more slowly in cold liquids than a thin simple syrup; dosed in small amounts to sweeten and add body.
Another concentrated sugar syrup of comparable thickness matches the sweetness and viscous body, but a refined-sugar syrup cannot reproduce the retained whole-cane-juice aroma where that character is the point.
Molasses
Molasses is the concentrated byproduct left after sucrose has been crystallized out of boiled cane juice, making it darker and more bitter; cane syrup is the whole reduced juice with nothing crystallized out, so it is milder and sweeter.
Raw sugarcane juice is boiled down until it reduces to a viscous syrup, retaining all of the sugars and other juice solids rather than separating out sugar crystals.

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