Many thanks for the welcome... Branson, if you look at the English and French billhook catalogues, you will see a great variety of shapes. The vast majority have a hook (or beak) but there are those with straight blades, and even those with convex blades. What was originally a tool used in the vineyards of ancient Greece to prune vines, became a Roman tool to cut and sharpen the stakes used to hold them up. Each task requires a different blade shape - to sharpen stakes on a block, the beak would get in the way, but it is necessary for vine pruning, or the blade will slip off the vine...
In European languages the same word is often used for any sort of chopper, and a square bladed billhook may be indistinguisable from a meat cleaver (in poorer communities the same tool was probably used for both tasks - and many others). However, I accept that in Asian cultures, different names may be used - but even here there is considerable variation in blade shape (there are dozens of regional forms of Japanese nata and kama, some with a hook, some without, some single bevelled, some double...). Part of the fun for me is extending my knowledge base and sharing it with others, however, I am always open to discussion if someone disagrees with me when I am hypothesising...