Dead-soft wire is extremely malleable and easily forms into a multitude of shapes. The best use for this wire is wrapping or holding lightweight items.
Half-hard wire is malleable and easily forms into your desired shapes. It keeps its shape well under moderate stress and can be used for moderate weight-bearing jewelry components.
Full-hard wire is malleable and holds its shape extremely well. I find this works best for clasps and holding heavy pendants or beads.
All three of these types come in different wire sizes, or gauges. It may seem backward, but the higher the gauge number the thinner the wire--meaning the finest is 26-gauge and the thickest, or heaviest, is 14-gauge. The most commonly used wire is 22-gauge. Use a higher-gauge wire, like 26-gauge, for projects that require more flexibility with delicate beads. Use a lower gauge wire, such as 14-gauge, for projects that require durability with heavy beads.