Open Burner Cooktops use air to feed the flame, which leads to faster boiling times. Since it's open it will be harder to clean than alternative burner types.
Sealed Burner Cooktops give you more control over the fire, but with slower heat times. However, they are generally much easier to clean than an open burner cooktop.
Smoothtop Cooktops use heating elements that are imbedded underneath a layer of opaque ceramic. They are electric and have many great features including the ability to bridge the elements together.
Coil Cooktops are electric. They are heated using an element that coils itself to form a semi circular circuit. They are considered to still be favorable because they are less expensive and still work great.
Modular Cooktops allow you to modify the heating elements. These units give you the choice to use different heating elements on the same cooking unit, allowing more flexibility and efficiency.