Separation is to separate different components of a mixture based on their physical properties by using distillation, evaporation condensation, filtration etc
for e.g. separating O2 from air which contains nitrogen CO2 and helium. we use distillation.
Re-crystallization is used to purify solid compounds by dissolving them in a suitable solvent and allowing them to recrystallize, leaving impurities behind. for e.g dissolution of the solid in a hot solvent, filtration to remove insoluble impurities, and slow cooling or evaporation to allow the compound to recrystallize.