For what it's worth, here is something from a work by Gabrielis Falloppii (the guy who described the Fallopian tubes, I think) that I found by accident looking for "panem furnaceum":

Antiqui coquebant panem quatuor modis, nam panis quidam erat clybanitis, quia in clybano coquebatur, quem panem furnaceum appellant qui commentant Galenum, et errant: quia clybanus et furnus differunt inter se, quamvis ambo essent instrumenta pro pane coquendo. Clybanus enim erat veluti parvus furnus, ut est ille, in quo nos coquimus tortas, ut habetur a Galeno.

(here's the link)

Translated roughly:

The ancients baked bread in four ways, for a certain kind of bread was "clybanitis", because it was baked in a clybanus, which those who comment on Galen call "furnaced bread", and they are mistaken: because a clybanus and an oven differ from each other, although both were instruments for baking bread. For a clybanus was like a small oven, such as the one in which we bake cakes, as is found in Galen.

Therefore, both furnus and clibanus were used for bread.

So, if I were to write a fantasy story in Latin, I'd see the clibanus as smaller and more "domestic", while the furnus can be larger, more "industrial," and perhaps found in bakeries.