Making syrups from trees other than maples is very similar to making maple syrup. Trees are tapped and sap is harvested during winter dormancy, and some combination of reverse osmosis and evaporation (typically using heat) is used to process the sap into syrup. Each type of tree, however, has its own quirks that make syrup production slightly different than syrup production from maples. Any deciduous, woody plant within a genus can be used to make a particular type of syrup. For example, any deciduous woody plant in the genus Betula can be used to make birch syrup.
Prolonged exposure to high heat can impart a burnt flavor on many different types of syrups if fructose is present in large amounts. Thus, reverse osmosis, which uses pressure instead of heat to concentrate sap, is a nice alternative to the traditional method of using high temperatures to remove water by evaporation. Some amount of heat is nice, though, to caramelize the sugars.