I am sure we haven't all seen everything .

My original Chinese heater has a piston pump and to be honest I just took it to be that they would all be piston pumps and required a degree of lubricant and not diaphragms. Diaphragm pumps will certainly be cheaper to produce but not as accurate on the metering.
Taken from Kemso fuel pumps.
Common Types of Diesel Heater Fuel Pumps
While the core electromagnet-driven pumping principle remains similar, designs vary:
- Diaphragm Pumps: This is the most common type found in modern diesel heaters. They use a flexible rubber or synthetic diaphragm sealed against the pump body. Solenoid action flexes the diaphragm to create the pumping action. They are generally simple, reliable, cost-effective, and handle low pressures well.
- Piston Pumps: Some heaters, often larger models or older designs, use a small piston moving in a cylinder. Solenoid action moves the piston. These might offer slightly higher pressure capability but are less common today in smaller auxiliary heaters.