Resting state functional magnetic resonance imaging (rs-fMRI) in infants enables important studies of functional brain organization early in human development. However, rs-fMRI in infants has universally been obtained during sleep to reduce participant motion artifact, raising the question of whether differences in functional organization between awake adults and sleeping infants that are commonly attributed to development may instead derive, at least in part, from sleep. This question is especially important as rs-fMRI differences in adult wake vs. sleep are well documented. To investigate this question, we compared functional connectivity and BOLD signal propagation patterns in 6, 12, and 24 month old sleeping infants with patterns in adult wakefulness and non-REM sleep. We find that important functional connectivity features seen during infant sleep closely resemble those seen during adult sleep, including reduced default mode network functional connectivity. However, we also find differences between infant and adult sleep, especially in thalamic BOLD signal propagation patterns. These findings highlight the importance of considering sleep state when drawing developmental inferences in infant rs-fMRI.