What is difference between betel nuts and nutmeg?

Broadly, nutmeg is from an evergreen tree whereas ginger is the root of a perennial plant. Both are used to flavor foods, and may be used together in pumpkin pie and molasses cookies. Both may be used as flavoring to render medicines more palatable. Both are native to Asia.

Nutmeg (genus: Myristica) is a hard seed, with a somewhat sweet, nutty flavor.It is generally grated finely and added to sweets (cookies, pies, etc), dairy dishes, vegetable dishes, and certain beverages such as eggnog and mulled cider. Species are mostly native to Asia and Australia, but are also extant in the Caribbean.

Ginger root (genus: Zingiber) is actually the underground stem, or rhizome, of the ginger plant. Ginger's flavor is both hot and savory. Each manner of preservation yields a subtly different flavor-- more or less hotness, more or less subtlety of other flavors. It can be chopped and used fresh in cooking or salads, thickly sliced of cubed and candied (sugared), thinly sliced and pickled, or dried and powdered, or dried and made into tea. In non-allopathic medicine, it is used for digestive ailments, Arthritis, colds, and to reduce inflammation. Species are native to South Asia, Southeast Asia, and Africa.