This is part of a broader syndrome of acne, with comedones and other inflammatory lesions present, whereas a furuncle is a solitary, deep bacterial folliculitis (abscess).
HS is a chronic, relapsing condition of recurrent abscesses, sinus tracts, and scarring in intertriginous areas, a much more extensive process than a single furuncle.
This presents as a tender, inflamed nodule resulting from the rupture of a pre-existing cyst, a different origin than a primary bacterial infection of a hair follicle.