A wandering mind is not always a creative mind. Anecdotes about ideas spontaneously entering awareness during walks, showers, and other off-task activities are plenty. The science behind it, however, is still inconclusive. Creativity might result from how thought context--whether thoughts are on-task or off-task--relates to thought dynamics--how thoughts unfold. To explore this, study 1 (n = 85) surveyed creative professionals about a single idea they had earlier in the day. The spontaneity of thoughts positively correlated with self-reported creativity, whereas off-task thoughts or doing something else did not. Study 2 (n = 180) replicated these findings in a student sample during an idea generation task and added that free movement of thoughts also correlates with self-reported originality during idea generation. As indicated by expert ratings, no relationship of thought dynamics and thought context was found with population-level creativity. Herewith, this study suggests that thought dynamics, rather than thought context, explain the often suggested relationship between mind wandering and creativity.