Cane syrup is simply clarified sugar-cane juice, boiled down to a syrup in much the same way maple syrup is made by boiling down the thin, sucrose-rich sap of the North American sugar maple and black maple trees.
Black birch trees also have a sweet sap that can be boiled down into a syrup.
Treacle is a term used mainly in Great Britain. Dark treacle is similar to blackstrap molasses and has blackstrap’s somewhat bitter taste.
Light treacle, also known as golden syrup (a significant improvement in nomenclature), is essentially cane syrup. The most popular brand, Lyle’s Golden Syrup, can be found in American specialty stores.
Sorghum is made neither from sugar cane nor sugar beets, but from a grass-like cereal grain plant with tall, strong stalks. It is grown around the world in hot, dry climates, mostly for use as hay and fodder.
But some varieties have a sweet juice in the pith inside the stalks that can be boiled down into a syrup.
The resulting product is called either sorghum molasses or sorghum syrup or sometimes just plain sorghum.