So I found one forum post relating to my issue :
After reading this and trying something - I did manage to make some progress…
After freshly booting up Slicer and uploading the DICOM data, I then clicked “Load” on the bottom of the Slicer interface and it loaded the DICOM files (which I think allows me to view their contents) and each scan appeared under the “Loaded Data” window in the left sidebar.
After that, when I clicked “Save” (from under “File” or Ctrl + S) I had the option of saving multiple files as .nrrd. (But not the whole of the data). I was able to find the files in the directory I saved them to.
So maybe I was running into difficulties because the DICOM data I was importing was from multiple different CT scans, and I had to load them first so it recognized them as multiple scans to be saved as multiple .nrrd files?
I just want to make sure I did this correctly in accordance with the tutorial I linked in my first post, so let me know.