Yes, the actual refrigeration and heating cycles are always based on compressing and decompressing a gas. But the gasses used differ based on temperature range, and further you can have air to air, air to water, or water to water for the heat transfer. The overall costs are the system can be very different based on whether you have a split unit that requires a single wall penetration, a central unit in the basement with ducting, or a geothermal system that requires digging deep trenches or wells. It makes for difficult conversation when some people are talking only about air to air minisplits when others are including all of these and more.