Both signal detection theory and just noticeable differences are components of psychophysics, or the study of the relationship between physical characteristics of particular stimuli and the sensations they produce.
Signal detection theory is a mathematical theory that relates to the ability to discriminate a particular signal from co-occuring sensory input. This theory also considers the individual's willingness to report the detected signal. According to this theory, every stimulus requires discrimination between signal (stimulus) and additional stimuli (consisting of both background stimuli and random activity of the nervous system). This theory also emphasizes that sensory experiences involve additional factors such as motivation and experience, other than just activity in the sensory systems. Psychologists use signal detection theory when they want to study behavior under particular conditions. For example, a researcher may be interested in how driving with loud music impacts the driver's ability to hear an emergency siren.
The concept of just noticeable difference refers to the smallest change in the magnitude of a stimulus that a person is able to detect. This is different than signal detection theory (SDT) since SDT involves distinguishing a signal from other stimuli while just noticeable difference involves distinguishing the actual change in the magnitude of a stimulus. Just noticeable difference is a concept that is often used by advertising and marketing executives. For example, manufacturers may want to know how much they can change a product before the consumers notice a difference.