A twig is a small thin terminal branch of a woody plant. The buds on the twig are an important diagnostic characteristic, as are the abscission scars where the leaves have fallen away.here are two types of twig, vegetative twigs and fruiting spurs. Fruiting spurs are specialized twigs that generally branch off the sides of branches and leading twigs, and are stubby and slow-growing, with many annular ring markings from seasons past.