  We analyze recently compiled data on the production of open heavy flavor
hadrons and quarkonia in e+e- as well as pp and p-nucleus collisions in terms
of the statistical hadronization model. Within this approach the production of
open heavy flavor hadrons is well described with parameters deduced from a
thermal analysis of light flavor hadron production. In contrast, quarkonium
production in such collisions cannot be described in this framework. We point
out the relevance of this finding for our understanding of quarkonium
production in ultra-relativistic nucleus-nucleus collisions.
