Spherical and chromatic aberration are two different things, but they are both image defects resulting from the way light is transmitted through a lens.
Chromatic aberration has to do with color (chroma). In CA the colors of an image are distorted because the different wavelengths that form those colors do not all converge exactly upon the focal point. The refractive index of the lens, which mathematically describes its ability to bend light, varies with different wavelengths, so each color of light is bent at a slightly different angle, resulting in a image with rainbow effects or colored fringes of light where there should be sharp boundaries. You can see a good tutorial showing how it looks at the first link below. Because this is a problem inherent to all lenses, the modern fix is to correct the final image via computer manipulation.
Spherical aberration is a result of lens curvature. Short focal length lenses demonstrate it more strongly than longer focal length lenses do. What happens in SA is that the further an entering light ray is from the center of the lens, the less accurately it is bent toward the focal point. As a result the image will be presented with a blurry halo. Glass with a higher index of refraction is less prone to this problem than lower index glass, but it is present in all spherical lenses to some extent. Since the center of the lens is more accurate than the ouer edges, lenses of high diameter can be used and the light blocked from entering the margins of the lens.
Aspherical lenses are available which do not have any SA. These are ground with a "perfect" shape, where the curvature is varied from the center to the edges so there is inherent correction essentially built into the lens, but they are extremely expensive to produce.