Jute and Broombush have always been very similar in planting and crossbreeding, but I only recently noticed that Broombush seeds share the same icon as what are generally called "vegetable" seeds.
The plants you watch growing up correspond to a particular seed type. Vegetables grow up looking like how Chives do in the above picture. Fruity plants have their own appearance to go with their seed icon. Same with Chocobo foods. Same with grassy/flower/nut plants like Jute in the above picture.

But Broombush, bred very similar to Jute and obtainable from each other, and looking like Jute as it grows up, has a different seed icon.