The classification of a plant as a tree (ilan) or a vegetable (yarak) affects many areas of halachah: the blessings over enjoyment (borei pri ha’etz or borei pri ha’adamah), the blessings over fragrance (atzei besamim or isbey besamim), the prohibition of orlah (which applies only to trees), the prohibition of kilei zera’im (which applies only to vegetables), and the prohibition of kilei hakerem (interplanting in a vineyard—there is no need to distance grapevines from species defined as trees).

The distinguishing feature of trees:  Trees have perennial woody trunks
The distinguishing feature of vegetables: Vegetables grow anew each year and grow from the root

In the plot before you are various species over which the posekim have debated their classification for generations