Stucco and concrete are two of the oldest building materials, still in use and popular today. There have been improvements and variations in both materials over the years. Today both are generally created with portland cement, made from limestone that's been specially heat-treated. When mixed with water, cement hardens into a solid material and fuses with rock or another mineral for strength.
Stucco is "Breathable"
Stucco is cement, fine sand and lime mixed with water into a paste that's spread over a surface with a trowel or sprayed by a machine. It may be used inside or outside. It forms a hard, water-shedding "breathable" surface that lets moisture escape through tiny pores, so water that gets behind it will evaporate. This reduces the chances of rot or decay. It's a durable exterior wall finish in all kinds of climates.
Stucco is Decorative
A stucco wall is decorative, but stucco itself has no strength and cannot support any weight. A stucco wall must be supported by some load-bearing material, such as wood or concrete. Stucco can be applied directly to any masonry-based wall, such as brick, concrete or cinder block. Stucco can be applied to wood-sheathed walls in typical frame construction by adding a metal lath over the wood. It's usually finished in a rough texture.
Concrete is also made with a paste of portland cement and water, but has stone aggregate added for strength. The most typical concrete mix is a blend of cement, sand and gravel (aggregate) plus water. Water is the key ingredient--too much will weaken the mixture, too little will prevent it from being formed properly. Concrete solidifies with a chemical process of cement and water called hydration; it can take several days or even weeks for concrete to "cure" properly to its maximum strength.
Rock Is the Strength
Rock is what gives concrete its real strength. The gravel or other aggregate bears the weight; sand is simply smaller aggregate that fills voids between larger rocks to make concrete more solid. Concrete has great compressive strength--the ability to withstand heavy weights and downward forces. Unless it's supported with reinforcing steel, it has very little lateral strength, to resist bending or pulling pressures. The size of the aggregate determines the concrete's strength.
Differences in Applications
Concrete is typically used for foundations, basements and flooring in houses and other buildings. Stucco is almost always applied vertically to a wall, although--because it's a paste--it can be formed around curves and angles. Concrete can also be built into curves and other angles by using forms that support it until it cures to maximum strength. Stucco needs no form support because it's applied in thin layers.