The wiki page leaves out the source of the the 'point-free' nomenclature - category theory ( e.g. https://en.wikipedia.org/wiki/Pointless_topology ). The original game was talking about sets (or other similar objects) without talking about 'set membership'/'elements', whence 'point-free'; you want to only talk about functions between sets (or morphisms between objects), and build everything up from those.

Is 'tacit' an old term or a newer rebranding?

(edit: https://en.wikipedia.org/wiki/Whitehead%27s_point-free_geome... might be earlier than the category stuff, but not sure if it used the 'point-free' nomenclature, nor if it has a direct lineage to the later category theory stuff )