Having different types of calibration standards helps to cancel out the measurement error introduced by the use of connector adapters. If the DUT has a port type different from the one of the VNA, the use of "between series" connector adapters is inevitable. Using a calibration standard which mates with such adapter will move the calibration reference plane at (or close to) the DUT, "absorbing" the adapter in the calibration process. Speaking of calibration reference plane - the concept is very simple - the reference plane is the plane which divides the VNA-DUT system. Everything "behind" the plane belongs to the instrument and will be taken out of the measurements. Calibration is performed at the plane. Everything at or "in front" of the plane is treated as DUT and it will be measured. Often, calibration device can not be placed exactly at a specific plane inside the VNA's port connector or test fixture due to the standard's physical size and/or need for a connector. There is an electrical length associated with the cal standard (pin / mating plane to actual OSL plane) which will cause a small delay and phase angle error (such standards are called an "offset" type). To account for this phase shift, commercial calibration kits come with a floppy disk containing correction data for the offset among other parameters (for instance - the stray capacitance for an OPEN or the stray inductance for a SHORT). After calibration is performed and the corrections are applied to the calibration model, the reference plane is "moved back" and located at the port's mating plane. For this very reason, when a calibration standard is measured as DUT with already calibrated VNA, it doesn't look "perfect" - the VNA shows the standard's internal phase offset and strays.
An excellent technical article about calibration standard definitions by William Highton (Chemandy Electronics) can be found here.
The main reason for matching the calibration reference plane and the mating plane of the VNA test port connector is to allow industrial VNAs to measure whole assemblies and devices, including their connectors. In the N2PK VNA (at least with the original software) the reference plane is assumed to be where the physical OSL calibration takes place. Instead of adding negative offset to move the reference plane back to the mating surface of the VNA's test port connector, it is accepted that the plane is right at the rear surface of the calibration standard connector (the location of the actual Open-Short-Load). The error introduced by the electrical length of the pin inside the connector is not that great at lower frequencies - for instance, assuming teflon dielectric (VF ~70%) in a standard SMA connector used for a home-brewed calibration standard, an offset of 5 mm will yield about 0.5 degree phase error @60 MHz. Commercial calibration standards use air dielectric, but this puts greater mechanical requirements during the fabrication process. By calibrating the VNA so the reference plane is on the back of the cal connector and fully exposed, it is more convenient to measure a single component but it means that the DUT test fixture should be made of (or at least include) the same type connector as the one used for the home-brewed calibration standards in order to maximize the accuracy. The setup can be as simple as the component (DUT) is just soldered on the back of the "test fixture" connector, while measures are taken to minimize external error (minimal lead length). With SMDs, this approach works well as the device is practically located directly at the "reference plane" when the test fixture connector is from the same batch connectors used to make the OSL standards. Another method for calibration is to use the test fixture connector itself for calibration - for OPEN the DUT is simply omitted, SHORT and LOAD are created on the spot during each calibration step and finally the DUT is soldered (Still, stray C for the OPEN must be known)