The most common families or groupings of airfoils are:
Symmetrical – Top and bottom are exactly the same. This creates an airfoil without Camber, that also produces zero lift at a zero angle of attack. All other airfoils are cambered and will produce aerodynamic lift due to their shape moving through the air.
Semi-Symmetrical – Like the picture shown above, the top and bottom are similar but the airfoil has a slight camber.
Flat Bottom – Very uncommon in RC models, airfoil bottom is flat from leading edge to trailing edge. This shape provides a fairly high camber and results in high lift, but can be structurally weak and hard to effectively use on models.
Modified Flat Bottom – Flat from main spar to trailing edge. This is actually a semi-symmetrical airfoil, but it’s the shape most people think of when you say flat-bottom. This shape increases the camber of the rear section of the airfoil moving the center of lift aft, giving more gentle stall characteristics.
Under-cambered – Mostly used on gliders (and WW I aircraft), the bottom closely matches the top with just some space in between. This shape produces the most lift of any airfoil, but also the most drag.
Reflexed – The trailing edge turns up slightly causing the camber to change to negative toward the aft of the airfoil, giving a positive twist to the lift (positive to the front and negative to the rear). This type of airfoil commonly found on flying wings without a horizontal stabilizer.
It should be noted that airfoils which have the same basic shape within a family, will also have common flight characteristics. Any differences between them will be small and on the order of landing a little faster and not an immediate loop into the ground on take-off.