The most common type of filter for a small pond is the internal filter. It is a filter box that is installed before the pump, both filter and pump sitting on the bottom of the pond. These are often sold as kits including the pump, filter, and fountain heads. Some cheaper kits only have a small sponge instead of a full filter box. These cheaper kits are only suitable for the smallest ponds.
The main advantages for this type of filter are that they are cheap, easy to install and are not very visible. This filter type is usually less than half the cost of any other filter. Because the filter is before the pump, it prevents the pump from clogging. A spray-style fountain requires an internal filter to not clog up constantly.
The biggest downside is in how difficult they are to clean. In order to clean it you have to reach into the bottom of the pond and pull out the filter and pump to get to the pads. This isn't that big of a deal in small ponds, but it is still more of a pain than most of the other filter types. They also have a limited flow so they are not suitable for high output pumps (such as those used on larger waterfalls) and they are not able to keep up with large ponds.
The internal filter is ideal for small ponds and people who don't mind being hands on with their water garden. However, it is not well suited to larger ponds and high volume pumps.