Conceptual concreteness and categorical specificity are two continuous variables that allow distinguishing, for example, justice (low concreteness) from banana (high concreteness) and furniture (low specificity) from rocking chair (high specificity). The relation between these two variables is unclear, with some scholars suggesting that they might be highly correlated. In this study, we operationalize both variables and conduct a series of analyses on a sample of > 13,000 nouns, to investigate the relationship between them. Concreteness is operationalized by means of concreteness ratings, and specificity is operationalized as the relative position of the words in the WordNet taxonomy, which proxies this variable in the hypernym semantic relation. Findings from our studies show only a moderate correlation between concreteness and specificity. Moreover, the intersection of the two variables generates four groups of words that seem to denote qualitatively different types of concepts, which are, respectively, highly specific and highly concrete (typical concrete concepts denoting individual nouns), highly specific and highly abstract (among them many words denoting human-born creation and concepts within the social reality domains), highly generic and highly concrete (among which many mass nouns, or uncountable nouns), and highly generic and highly abstract (typical abstract concepts which are likely to be loaded with affective information, as suggested by previous literature). These results suggest that future studies should consider concreteness and specificity as two distinct dimensions of the general phenomenon called abstraction.