Digital imagery is commonly divided into raster and vector representations, yet the distinction is frequently reduced to the misleading shorthand that raster images are composed of pixels while vector images can be enlarged without loss of quality. For professional graphics work, the difference is considerably deeper. Raster and vector graphics encode visual information according to fundamentally different models: raster imagery records sampled values at discrete spatial locations, whereas vector imagery describes geometry, attributes, and relationships that must ultimately be rasterized for display or most forms of printing. This article examines the mathematical and practical foundations of both representations, including sampling, interpolation, aliasing, Bézier geometry, rasterization, resolution, compression, transparency, image tracing, technical illustration, photographic imagery, printing, and contemporary artificial-intelligence-assisted graphics. Particular attention is given to misconceptions surrounding resolution independence, raster-to-vector conversion, generative enlargement, and the assumption that a file format alone determines whether artwork is genuinely vector. The analysis argues that neither representation is intrinsically superior. Professional image construction instead depends upon selecting, combining, and preserving representations according to the visual information being modeled and the requirements of the final reproduction system.