Three competing theories of emotion
Psychology offers several models of how an emotion arises. The James-Lange theory, from William James and Carl Lange in the late 1800s, holds that a stimulus first triggers a physiological reaction (racing heart, trembling) and that the emotion is our perception of that bodily change: we feel afraid because we tremble, not the reverse.
The Cannon-Bard theory, advanced by Walter Cannon and Philip Bard in the 1920s, challenged this, arguing that the bodily response and the conscious emotion occur simultaneously and independently, both triggered by the brain (notably the thalamus), rather than one causing the other.
Schachter-Singer and the role of interpretation
The Schachter-Singer two-factor theory (1962) adds cognition: physiological arousal is general and somewhat ambiguous, so the brain must label it by interpreting the situation. The same racing heart could be read as fear or excitement depending on context. Emotion, in this view, is arousal plus a cognitive appraisal of its cause.
Each theory captures part of the picture, and later appraisal-based models built on the cognitive insight. The contrast is often summarized by which comes first: bodily change (James-Lange), simultaneous response (Cannon-Bard), or arousal interpreted by context (Schachter-Singer).