The typical acronyms and phrases are HDD for Hard Disk Drive and SSD for Solid State Drive.
The generic "parent" term is DD for Disk Drive.
Adding to this list is FDD for Floppy Disk Drive (remember those?), ODD for Optical Disk Drive (more common terms are CD, DVD & Blu-ray Drives though), Tape Drive and USB Flash Drive.
To answer your question though, there really is no opposite term, since hard disks aren't binary in their nature (yes pun intended)