HSP stands for Host Signal Processing, these modems are nothing more than a curcuit board with phone jacks, no work is done on the modem itself, EVERYTHING is done in software with your CPU. HSF stands for Host Signal Function and are exactlly the same as HSP modems.
HCF stands for Host Control Function, these modems are hardware modems for the most part, the only thing that seperates them from hardware modems is that they lack a controller (part that accepts AT commands and controls modem functions) The actual modulation/demodulation work is done on the modem, unlike the all software HSP and HSF "modems"
todpod: There isn't a Linux driver for HCF modems yet, Conextant promised one by the end of last year, but it has yet to show. They did however release a linux driver for their HSP chipsets. I've tried the HSP driver myself, it does make the modem go off-hook, but thats as far as it would go, wouldn't not dial at all. Nor would it hang up!