Although the formal dining room is also typically close to the kitchen, it is usually closed off with a door and is a separate space from the kitchen. A functional dining room can provide a dining space separate from the kitchen, but does not require a wall or door to define the separate space.
Functional dining rooms tend to be more popular in open-concept layouts while formal dining rooms are a better option for homeowners that want a clear separation between the kitchen and dining room. This can be helpful if you plan on entertaining a lot, especially if you have small children who may be resting or involved in other activities.