Are you sure she wasn't talking like "save your work to the hard drive" - which would make sense. "Log off your hard drives its the end of the lesson" wouldn't. Also in speech it's unusual to use acronyms but if I did I probably would say " h double d" or "H dee dee" either I
might (unlikley) use HD (rather just say hard drive) as after all "HD"[D] is hard disk [drive]. Your ICT teacher probably knows more than they let on. Most haven't got a clue about proper techy stuff but I guess most could still plonk a system together from bits even if they don't know what the difference is between 32nm and 40nm or PC2 or PC3

etc.
Talk to her tomorrow IRL. I thought it was only for HE or FE students really.