Hi. There are many different families of octopus, but that with which most of you are familiar is Octopodidae (your typical benthic octopuses). In this family the distalmost portion of the male's third left OR right (but never both) arm is modified into a thumb and shovel-like structure, the calamus and ligula, collectively referred to as the hectocotylus. In some shallow-water species, particularly those related to Octopus vulgaris (or referred to this 'complex'), this hectocotylised portion is very small and not always easy to see with the naked eye, especially in juveniles; the male also has a thickened portion of web running the length of either the third right OR left arm (but again, never both) called the spermatophoral groove. In some other types of benthic octopus, genera like Pinnoctopus and Enteroctopus, the terminal portion of the male's third right arm is enormously developed, as is the spermatophoral groove, and external sexing of the animal is quite easy. In yet other types of benthic octopus the male possesses one or two grossly, abruptly enlarged suckers, usually along the mid-portion of the arm, but this is certainly not a common characteristic in these animals.
In different families of octopus, usually the pelagic families (Argonautidae, Ocythoidae, Tremoctopodidae) the entire male's third left OR right (again, never both) is encapsulated in a specialised pouch that detaches from the adult and 'swims' (or is implanted) into the female's mantle, where it lodges around the base of her gills (proximal to her genital apertures); the male then beats a hasty retreat (before being devoured). In the Haliphronidae (=Alloposidae) the male's arm is actually recessed in a pouch at the base of the arms, almost enclosed within the head, from which, I believe, it protrudes, breaks free and again swims into the female's mantle cavity (the male would appear to have 7 functional arms) [Haliphron is a difficult animal to describe). In the cirrates (finned octopuses) the male can (this is not always the case) have grossly enlarged suckers at certain points along the arms, or on several arms (rather than on each); this is not uncommon in species of Opisthoteuthis. Otherwise I am not aware of any major morphological difference between males and females of other cirrate genera (that's not to say that they do not exist!); I'd be mighty impressed if you had one of these in an aquarium!
One day we'll get organised and get more information online; time is always the problem.
To make it sound more simple incase, male octopuses usually have overly larger sucktion cups underneath their arms used for competition amongst other males in a mating process or winning over females. They show off their larger suckers to ward off other males and there visible externally. Females have ordinary suction cups...each the same size as the other and normal arms with no reproductive limb.