Well...sure, you could put bigger storage on a mainframe. It's just money, after all. But you could put a tape drive on a home computer. And bigger disks. And a card reader, for that matter. Where the 360 really crushed the home computer was in aggregate bandwidth, via the Channel architecture. An Apple 2 could just about keep up with a floppy and a display. A 360 could keep up with dozens to hundreds of tapes, disks, card readers, terminals, printers and other things all at the same time.
Large storage compared to memory meant a lot of focus on external memory algorithms
I would agree with that. I would just argue the real mainframe advantage is a whole-system one and not point to a single factor (memory size).
Edit: apparently these cartridges actually are 18TB, 45TB is "compressed" capacity. Still though, terrible marketing aside it's still factor of 225,000.
An IBM 360/20 on the small side, however, ranged from 4kB to 32kB which was similar to home computers circa 1980, before it is routine to have a complete 64kB address space.
Where the 360 crushed home computers was in mass storage, 9-track tapes could store 80MB contrasted to floppy disks that stored less than 200kB. Large storage compared to memory meant a lot of focus on external memory algorithms, also there was already a culture of data processing on punched cards that translated to the 360 (e.g. terminals have 80 columns because punched cards had 80 columns)