Clothing is a little more difficult. Clothing does have to be individually modeled, but it doesn't make sense to model the clothing separate from a fully detailed body. It can create some major problems when animating. First you'd have to animate the body; then you'd have to animate a second time to make the clothing's animation follow the body so that the character appears to be "wearing" the clothing. This can cause problems with matching key points, with timing the animation, and with adding way too many polygons and textures to a final render, thus drastically increasing rendering time and power.
Instead the clothing and the model are created all in one piece. The easiest way to think of it is to compare it to a plastic-molded figure. It's all one solid piece, but clothing details are extruded out from the surface - anything from the raised edge of a coat lapel to the flare of the coat around the legs. Applying color helps to differentiate them from the main shape. You can actually achieve an amazing level of detail this way, especially using texture mapping to enhance the materials of the clothing. By modeling the clothing as part of the body, you don't have to worry about animating the clothing following the body. You just have to animate the polygons that don't conform to the body, and follow their own rules of motion depending on the type of material. Some finer details, things like jewelry and other small pieces, may be modeled separately for convenience, then linked to the main model.
In some 3D animations you'll see characters changing outfits and hairstyles. For this animators will create separate 3D model with the changes incorporated into the model, rather than applying changes to the existing / default model. The model is then swapped into the scene and used in place of the default, so it looks like you have the same model with a different wardrobe.
However, playable models in video games can take a different approach, especially models that allow you to customize your character's appearance and clothing. More often than not things like clothing, facial changes, and coloration are mapped on, using texture images and bump maps that conform to the shape of the model and provide all detail via the artwork painted on the map. When you pick the option to change these features, the game just swaps the map without changing anything else about the model. Hair can be a little more complex; sometimes the different hair types are created as separate objects linked to the main model, and changing the hair options just swaps out which option is linked. The same can be said for various accessories.

