It is possible to save images to a memory card, as well as saving to your workstation, with supported Canon and Nikon cameras. You may find this works with other camera brands, but it is dependant on the settings available, as well as the camera firmware being used.
You can activate this by going to the Tether tool tab > Camera Settings and then changing the following option:
Tether (tool tab) > Camera Settings > Save To
The name of your memory card will change depending on what type of card it is you are using. In this instance, a CF express card was being used.
This provides a convenient backup method, as well as enabling you to see and review the images on the camera display. This functionality is also available when using wireless tethering.
N.B. Enabling this feature will affect the waiting time when connecting the camera, as your operating system will index the content of the card. The more images that are on the card, the longer this can take.
Other camera brands
Some cameras have the ability to save images to a memory card during tethering. Those are Sony A7 III / A7R III / A9 and some Fujifilm cameras, dependant on individually adjusted camera settings and the camera firmware. This functionality however, is only fully supported with Canon and Nikon cameras.