In Bedrock Edition, either kind of campfire can also be broken by pushing it with a piston or sticky piston. If mined with a tool enchanted with Silk Touch, the campfire instead drops itself as an item. A regular campfire drops 2 or 4 charcoal, a soul campfire drops soul soil, and either one also drops any items placed on it.
Campfires can be mined with any tool, or without a tool, but axes are the fastest.