Yes, as far as I can tell the footprint of pyrolysis portion is basically the same (various wild seeming claims notwithstanding) though I haven't dug into this deeply, and specifically haven't looked into it in over a decade.

However on a full cycle basis the difference is biochar is typically made from local material (mostly the leftover waste from the prior year's harvest) which is right there (zero transport) and would otherwise rot and release methane and CO2 on its own, even if plowed into the field.

Charcoal is made from trees, typically cut down and transported to a factory and then transported to the customer.

In general I am not in favor of burning trees, enjoyable as it is on a cold night out in the forest.