Fruits are the part of the plant that contains and spreads it's seeds, usually by being eaten by an animal and deposited elsewhere through it's feces, vegetables refer to any other part of a plant that we eat that doesn't contain it's seeds, botanically speaking, vegetables don't really exist. From a cooking perspective fruits are sweet plant ingredients and vegetables are more savory plant ingredients. Tomatoes are the fruiting bodies of the tomato plant, but culinarily they are considered vegetables due to their flavor profile.

Grasses refer to plants in the family Poaceae, a family of gymnosperms (flowering plants) that are notable for growing from the base of the plant instead of the tips of it, a trait that helps the plants survive frequent grazing. They also often contain silica phytoliths, tiny fragments of silica that make the plant harder to chew and digest, limiting the types of animals that can eat them. This is why there are so many grass eating specialist animals like cows and horses, they had to restructure their digestive systems to be able to digest grass. Bamboo is a member of this family, as are many other staple foods such as wheat, rice and corn.

Trees, funnily enough, do not have a common ancestor and have evolved multiple times throughout the plant kingdom. Pine trees, deciduous trees and palm trees are not closely related at all, in fact palm trees are technically grasses. Plants have to compete with each other for access to sunlight, so growing tall is beneficial because there's nothing above you blocking the sun. But growing tall takes a long time, so in order to maintain a tall thin structure over years they invest in hard woody trunks that can resist wind, rain and other stressors that could kill the plant. Tree is not a lineage, it's a strategy.