What are the uses of fan shaped brushes and finger shaped brushes?

Question

What are their use cases?

The fan shaped brush:

The finger shaped brush:

Answer 1

• The fan-shaped brush is perfect for blending oil paints. I use it to either blur fresh paint (be it an area or a detail) into the background, or to create a smooth gradient between paints.
  When painting with very fatty paints, or simply a lot of paint, this brush will lose its efficiency, as it is too thin and fine to manipulate, accumulate, or contain much paint.
  I have no experience using this with acrylic paints, but can imagine it will work similarly, when using little and diluted acrylics.
  With this brush it is especially important to clean it regularly, as it loses this functionality whenever there is the slightest irregularity (leaving obvious marks in the paint surface).

• With the comb, rake, or fingered brush I have a slightly similar experience: it can be used to blend areas or details while maintaining a certain amount texture (resulting in a 'broken' gradient, if you will).
  It's also an obvious contender for painting details like vegetation (grass, reeds, branches, &c.) and hairs, as it naturally leaves lines.
  It can also be used for graining or painting imitation wood (although those brushes are usually larger).

Answer 2

The fan brush is also very useful to paint lots of fine texture.

Bob Ross often used a fan brush to paint bushes or foliage on trees and waterfalls. You can use the same technique to paint either a rough texture of numerous tiny dots (like distant grass, leaves, rock, sea foam) or a smooth texture of fine, parallel lines (like hair, fur, water, grass and others).

For the technique to work the bristles must be hard enough to hold their fan shape even when they're wet with paint and water. If the bristles clump together once they're wet, you get a much bigger texture that resembles that of the comb brush.

The comb brush achieves similar effects (several parallel lines with a single stroke), but not as fine as the fan brush. It's useful for grass, fur, hair or woodgrain textures that are in the foreground of the painting and therefore more detailed.