Filtration separates an insoluble solid from a liquid. The solid is caught in the filter paper (the residue); the liquid passes through (the filtrate).
Evaporation gets a dissolved solid back from its solution. The water is heated away, leaving the solid crystals behind.
Distillation collects the liquid itself from a solution. The liquid boils, the vapour is cooled in a condenser and collected as pure liquid.
Chromatography separates dissolved colours or dyes. They travel up the paper at different speeds because some are more soluble than others.