I've just been doing some reading and it seems adventitious roots (those formed on cuttings from stem tissue) can arise from several places/tissues in a stem.
Some species of plants that are easy to root have what are known as latent root initials already in their stems. These are areas of cells that will begin dividing when/if they are needed - as in when a branch is removed from a tree. I suspect figs have these perhaps beneath nodes.
There are other plants where these (latent) root initials are visible on the external stems as little nubs - examples are Philodendron, tomato, Coleus. (The use of the terms root 'primordia' and 'initials', (even internal 'callus') over-lap and usage seems to depend on which text you are reading.)
Callus tissue is formed when relatively unspecialized cells resume cell division and a mass or lump of tissue is formed. These can arise from several places within a stem, but apparently mainly from the food conducting tissues (phloem), cambium, ray cells, etc. When a stem is cut, in the correct circumstances callus formation can be seen at the cut as little bulges around the base. Sometimes in high humidity, also at the top of a cutting.
While some species form roots from callus, it is not required for adventitious root formation. And some plants form callus at a basal cut, but new roots actually develop on the stem above the callus. If you look at photos of roots emerging from fig cuttings, they often are seen just above the bottom of the cutting (often just below a node, but sometimes scattered along internodes.)
Regardless of terminology, the process involves getting cells in a dormant cutting to begin actively dividing and eventually developing into roots. There seems to be much variety in root formation across the plant world. My guess is figs, which are generally easy to root, utilize more than one anatomical avenue. Just my guess.
As to whether a cutting should be freshly cut prior to rooting, I don't know. There are many species of plants that root better when the stem has been wounded (often with a razor blade slicing off a thin, 1 inch fillet at the base - sometimes on both sides of the stem).
This is general information and not necessarily fig specific. Much is unknown.