If the airplane is designated as an amphibian, it can takeoff and land on land or water. There are a few airplanes (DHC-3 Otter, and some PBY Catalinas) which are water only planes, yet can be fitted with beaching gear, which once fitted while floating in the water, allows them to taxi or be towed out. Beaching gear is not suitable for landing and takeoff (no suspension). There are some airports which are both floatplane bases, and have runways. These airports are valuable for seasonal change over of floatplane to be wheel planes. Though amphibians do ramp in and out of the water, it would be common for an amphibian pilot to choose the use of the runway over the water, unless they are simply having water fun. A common reason to land an amphibian at an airport is for fuel, which is more easily put in with the plane on the ground than in the water.
Amphibians are typically heavier than the floatplane equivilent, as well as being more expensive to buy, maintain and insure. However, it is nice to be able to not leave the plane floating in the water for long periods, accumulating gunk on the float bottoms, and risk of sinking. It is common for city dwelling pilots to own an amphibian, which lives at the local airport, and provides weekend transportation to water destinations. A few small airlines use them this way too, a Toronto operator, for example:
Muskoka, Toronto | Float Plane Services | Cameron Air Service Ltd.