I believe introversion is a fundamental character trait where as shyness is an environment conditioned behaviour subject to the personality development.
I agree that the "state/trait" distinction (contextual/foundational) relates to this issue. The reason that measures may overlap is that many of the ways to measure both introversion and shyness rely on subjective surveys, and thus contextual issues may influence such measures along with foundational personality characteristics. Precise wording for surveys and statistical methods can reduce such overlap, but it would be difficult to eliminate it entirely. Shyness describes behavior(s) that most introverts would tend to engage in, so "common method variance" would be difficult to reduce to zero. Any publications on the "Big Five" personality trait dimensions or the influence of in utero exposure to stress on personality development could be relevant.
I reviewed relevant empirical evidence in my book, Understanding Shyness: Psychological Perspectives (Palgrave, 2001), Chapter 1. Questionnaire measures of shyness and introversion do overlap but they predict observed behaviours differentially. See also a chapter by Louis Schmidt and Arnold Buss in The Development of Shyness and Social Withdrawal edited by Kenneth H. Rubin and Robert J. Coplan (Guilford Press, 2010, pp. 23-41). Susie Scott discusses this issue from a different perspective in her book Shyness and Society (Palgrave Macmillan,2007) drawing upon interviews with self-defined 'shy people'.