The suitability of a vacuum pump depends on both the intended application and the specs of the particular model regardless of the type of pump. For vacuum chucking on the lathe, where the requirements aren't very stringent you can find suitable pumps in all three categories. But, you can generalize about the characteristics of the three categories. Piston pumps are capable of pulling a hard vacuum and are the best for HVAC use, but the flow rate isn't high and lubricant is in the flow stream. Diaphragm pumps pull a soft to moderate vacuum with a flow rate that is between the piston and rotary vane pumps. Rotary vane pumps pull a high vacuum that typically isn't quite enough for HVAC applications and they have a high flow rate. Rotary vane pumps come in two flavors ... lubricated and dry. You can find a lot of performance variation in each category as well as a lot of overlap between the three types of vacuum pumps. While on average the dry rotary vane pump looks like the best fit for woodturning vacuum chucking, we can't exclude all diaphragm and piston pumps because there are plenty of models that will fit the needs of vacuum chucking. Also, the "requirements" of vacuum chucking are soft requirements that are somewhat overstated to give a lot of safety margin. In the early days of vacuum chucking some people used shop vacs and found them to be perfectly suitable (soft vacuum, but huge air flow that can overcome lots of leaks) ... the problem was that the shop vac motor, starved of cooling air, would burn up from lack of adequate cooling air. These shop vac systems also used simple rotary couplers that were just a slip fit between two cylinders.