From what I know, intuition is affect-based. But how do they differ?
Affect is a fundamental feature of consciousness and is a mental representation of input from the body to the brain. Affect corresponds to feelings of (un)pleasantness and activation (arousal).
Emotions are conceptualizations (interpretations) of your affect in a given context. You might feel pleasant and highly aroused (an affective feeling) on a roller coaster, and your conceptualization of that affect in that context would be "excitement" (an emotional feeling). In this sense, emotions are what we would traditionally consider to be "cognitive."
Under this scheme, intuition doesn't really have a direct, formal relationship to affect or emotion, although intuitions are often affective (well, pretty much everything is affective). But see here for a more informed discussion of the literature.
the experience of feeling or emotion. (Hogg, et al. 2010)
any relatively brief conscious experience characterized by intense mental activity and a high degree of pleasure or displeasure (Cabanac, 2002; Schacter, 2011). Scientific discourse has drifted to other meanings and there is no consensus on a definition.
An emotion can be an affect as a result of intuition
Hogg, M.A., Abrams, D., & Martin, G.N. (2010). Social cognition and attitudes. In: Martin, G.N., Carlson, N.R., Buskist, W., (Ed.), Psychology (pp 646-677). Harlow:Pearson Education Limited.
Schacter, D. L., Gilbert, D.T., Wegner, D.M. (2011). Psychology Second Edition. New York, NY:Worth Publishers. p. 310. ISBN 978-1-4292-3719-2.
Intuition: my environment is totally uncorrelated with anything I am aware of but it still leads me to believe something is about to happen.
Emotion: a state of mind evoked by physical sensations, particular memories, and expectations of the future.
Affect: the outward manifestation of my emotions which may or may not be deliberate.