What is the diffference between landing lights, taxi lights and external lights?
There are basically two types of (exterior) lights in an aircraft- the navigational lights, which are required to be switched on from sunset until sunrise and other forms of exterior lights, which can be switched off at the pilot or operated only at some parts of the aircraft operation, like the landing/taxi lights. 

A (non-exhaustive) list of aircraft lights:


Navigation lights All aircraft are equipped with a steady light near the leading edge of each wingtip. The starboard light is green while that on the port wing is red. The different colors make it possible for an outside observer, such as the pilot of another aircraft, to determine which direction the plane is flying. These are required to be on during operation (in night).
Navigation or Position lights In addition to the red and green lights, most large planes like airliners are also fitted with other steady white navigation lights in various locations like the trailing edges of each wingtip, horizontal tail and top of the vertical tail. The main purpose is to increase the visibility of aircraft from behind.
Anti-Collision Beacon lights These are are flashing (or strobe) light assemblies installed on the upper and lower fuselage of aircraft,used to improve visibility of the aircraft. These can be switched off at the discretion of the pilot under some conditions.
Strobe lights High-intensity strobe lights that flash a white-colored light are located on each wingtip. These flashing lights are very bright and intended to attract attention during flight. They are sometimes also used on the runway and during taxi to make the plane more conspicuous.
Logo lights These steady white lights on the surface of or at the tips of the horizontal stabilizer are used to illuminate the company's logo painted on the vertical tail. These are usually switched off in airports to improve the visibility of the aircraft.




1) Navigation lights 2) Aft light 3) Anti-collision strobe lights 4) Logo light
"Jet-liner's lights 1 N" by CC BY 3.0 via Commons.


Wing lights Many airliners feature lights along the root of the wing leading edge that can be used to illuminate the wing and engine pylons in flight. These lights may be used to make the plane more visible during takeoff and landing or to inspect the wings for damage in flight. Pilots can also use the wing lights to inspect the wings and slats for any ice accretion that might build up when flying through clouds.
Taxi lights A bright white lamp is located on the nose landing gear strut of most planes. This light is typically turned on whenever the aircraft is in motion on the ground for greater visibility during taxi, takeoff, and landing.
Landing lights Typically the brightest light in the aircraft, these are fitted on most planes (and helicopters) for enhanced visibility during the landing approach. These lights can also be used to illuminate the runway at poorly lit airports. They can be located in the wing root, in the outboard wing, or somewhere along the forward fuselage (the usual location incase of helicopters), with some aircraft having them in more than one location.




Boeing 787 Lights; Source: captalk.net


Runway Turnoff lights Usually located in the leading edge of the wing root, these bright white lamps are intended to provide side and forward lighting during taxi and when turning off the runway. These lights are most useful at poorly lit airports but are usually unnecessary. The lights can also be used in flight if greater visibility is required.
Wheel Well lights Some planes are equipped with additional lights in the nose and main gear wheel wells. These lights are provided primarily to assist ground personnel in making pre-flight inspections of a plane at night. 


The image below shows the lights in a Boeing 737.



Image from staticflickr.com