Combustion engine driven compressors are similar to electric motor driven ones, but are more complicated and certainly have plenty of moving parts. Adsorption/absorption refrigeration systems have fewer moving parts, as they use heat as the main driving force and so don't have compressors. But they still have moving parts like pumps and fans, and they are completely dissimilar in design to mechanical compressor driven refrigeration.
My old 1975-era RV fridge had no moving parts at all, no pump, no fan. Just a propane driven pilot light which switched off & on as it heated the ammonia in a sealed system. The ammonia circulated passively. The fridge had to be kept in a more or less vertical orientation for the circulation to work properly. Too much off level, it wouldn't work. When the RV was rolling down the road, the orientation of the fridge was less important, the constant shifting back & forth of the fridge would allow the refrigerant to circulate quite well. Its main point of breakdown was the pilot light / thermocouple mechanism, kept either getting dirty or corroded, otherwise it was extremely reliable. The propane supply could be switched off and the fridge could run on "shore power" - 110VAC when the RV was plugged in. The 110VAC was simply used as a heat source, again, no pumps, no fan, electricity was solely used as a heat source.