I’m familiar with “hit or miss” engines, also known as boat engines, but had not heard of engines that do both. Hit and Miss seems like an odd name for an engine type, not exactly inspiring confidence.
These flywheel engines would fire, or hit, only as needed to maintain operating speed and would skip combustion cycles, or miss, allowing the engine to coast under its flywheel inertia until power was needed again. Hit and Miss engines fail to fire on purpose!
Here’s an interesting video of an old John Deere Hit and Miss engine driving an ice cream churn. It chugs and sputters a lot and occasionally goes POP when it needs more power.