I'd been doing it for decades before I been knew it had a name; I just thought of it as splitting or cutting wood with my knife.
No, you do not need a saw-cut stick to baton, either as the baton or the stick. But it does look better if you're doing a video, I guess. But you can split via batoning any old stick, etc, you need to. Also by using your knife to carve some wedges, you can split quite large logs, etc. Batoning is just a forced wedge technique.
Note that you can also baton cross-grain, as if you were slowly chopping through the stick with an axe or hatchet. V-angles and all. that's how you make a long stick into a short stick!
Finally, only use a piece of wood to baton your knife; NEVER use a metal baton. You'll destroy your knife if you do!