Back to the LED quick: That type of LED is likely a single emitter die.
As others have said, it's not a transistor, but it
is a semiconductor material. It's a different material than a transistor, and it's doped with other elements to change the colors. There are two chemistries in common use for bright LEDs: InGaN and AlInGaP.
Indium Gallium Nitride makes blue and green LEDs, and AlInGaP makes red and yellow. (Almost yellow, anyway. It's kind of on the orange side though.)
A white LED uses a blue emitter and a yellow phosphor. Some of the blue excites the phosphor to produce yellowish light, and some of the blue passes through. To your eye, the combination of yellow and blue looks white. Manufacturers will vary the amount of blue and yellow light in order to change the way the color of the white light looks.
Small LEDs like that will often have a single die.
Larger white emitters can incorporate multiple dies in order to increase the overall brightness.
The Luxeon's CoB lineup uses this method: Beneath the yellow phosphor are multiple individual dies.
That's done to keep manufacturing costs low: If a single huge die was made, a flaw in it would effectively mean the entire thing would be scrapped. Using small dies means that any flawed components result in very little scrap. In addition, the die can be a standardized design that is used in multiple products. A small LED would only use a single die.
The dies themselves are often tiny.
This page shows a photo of an LED that's roughly 3x3mm.
The dark square in the middle is the only part that makes the light. The rest of it is packaging to direct the light outward, make soldering easier, and provide a path to conduct heat away from the die.
Here's an example of an LED that has multiple dies.
The gold wires are "wirebonds" that make electrical connections for positive and negative.