From DT Online
The Taxonomy of the plant Kingdom classifies trees as either Angiosperm (encased seeds) or Gymnosperm (naked seeds). These sub-divisions are each sub-divided into Genus (a subgroup of organisms that have many common characteristics such as oaks or pines) then Species which can be thought of as a specific kind of tree - but this too can be further sub-divided into Varieties for example.
Hardwoods include Deciduous trees grown in Temperate Climates such as ours (many hardwoods in Tropical Climates are Evergreen). They have broad leaves and are fruit-bearing or have seeds borne enclosed in cases - and so are classified as Angiosperms.
Examples growing in the UK include: Oak, Ash, Elm, Sycamore, Walnut, Birch, and Beech plus any Fruitwood such as Apple, Pear or Cherry. Non-native examples include: Mahogany, Rosewood, Teak, Ebony, Obeche, Ramin, and Jelutong. Balsa is also a Hardwood even though it is very soft - the distinction between Hardwoods and Softwood is not determined by how hard or soft they are.