What every brush icon symbol means

[Bellatrix]

Ball and Stick: Performs colour adjustments usually used in layer blend operations
Checkerboard: Texture brush
Cog: Meaningless; the two brushes that have this are completely different.
Pen: Size/Opacity settings have been changed from their default (remains even if changed back again)
Pixel: Creates solid pixels
Polka Dots: Coordinate-sensitive texture brush (one of these brushes should have checkerboard symbol instead)
Rotation: The brush is sensitive to stylus tilt, if supported by your tablet (possibly brush rotation too?). Not all tilt-sensitive brushes have this symbol.
Tricolour Balls: Convolution Matrix brush
Tricolour Hexagons: Meaningless. Only one brush has it, and a nearly identical brush does not.
Water Drops: Smears, if below 100% opacity