Trees need branches so that they can have more leaves for doing photosynthesis. If they only had leaves coming directly off the trunk, there wouldn't be as many leaves that could fit. Plus, the leaves that were higher up would block the lower leaves from getting light. Branches allow the leaves to be spread out and catch more sunlight.

The trunk does form from the sprout that comes up from the seed.

The other sprout grows down and branches out to form the roots. The roots make the tree more stable if they spread out under the ground.

Can you think of other reasons that roots should branch out? Think about what the roots do for the tree.

Branches are extensions of the main trunk and allow for trees to produce leaves away from the main stem. Some trees do grow straight up and you tend to find them in more Northern or Southern parts of the hemispheres where they get very low light amounts during the day (Alaska, Northern Canada etc). These trees grow tall, straight and dense. In more temperate and equatorial regions there is more sunlight from multiple directions so it's more advantageous for trees to grow in every direction and capture sunlight at different times of day.

It sounds like you are having some confusion over the words used to describe plants. Here is a great site to get oriented to describing plants: