Question
What is the difference between a Magnolia Tree and a Bay Tree?

Answer
There is always problems when we use common names. Some folks call Magnolias Bay.  Example: Magnolia grandifloria is Southern magnolia and Magnolia virginiana is Bay leaf magnolia. Common nmaes are used for different trees in different parts of the world.

In  science they both (magnolias and bays)  fall undeer the subclass Magnoliidae.  Magnoliidae (or magnoliids) are a group of about 9,000 species of flowering plants, including magnolias, nutmeg, bay laurel, cinnamon, avocado, black pepper, and many others. They are characterized by trimerous flowers, pollen with one pore, and usually branching-veined leaves.

Magnolias are under the order Magnoliales and belong to the family Magnoliaceae (about 225 species including magnolias and tulip trees).

Laurales is an order that contains the "bay Trees. The order includes about 2500-2800 species from 85-90 genera, which comprise seven families of trees and shrubs. Most of the species are tropical and subtropical, though a few genera reach the temperate zone. The best known species in this order are those of the Lauraceae (for example bay laurel or Laurus).

In layman terms they are cousins and are similar with magnolias having a larger flower.