Mild depictions of partially aroused men, not showing penetration.
Basically both words are 'catch all phrases' that encompass a wide variety or interpretation of what is, what isn't suited for that category.
Usually very sexually explicit content is rated as 'hardcore' while implied sexual acts are termed 'softcore'. This can also include non nude sites, which have models or characters posing in a sexual enticing or arousing style.
The infamous Calvin Klein underwear commercials are a prime example of softcore pornography.
The advent of the MPAA (Movie Producers Association of America) rating system helped define, in America, what was acceptable and what wasn't. It defined more of what could be shown publicly, though that has changed dramatically since its first appearance in 1968.
This rating system was brought about by pressure from various religious groups, concerned about the increasing display of violence and sexual connotations in movies, television.
Other nations, had versions of this system before the MPAA created it's version.
A wide range of poses or states of dress, undress, can be classed as softcore.
Usually, it is more of an implied sexuality, that gets the photograph or video rated as softcore. The alluring pose, or state of semi undress may titillate, arouse even, but as no genitals are clearly shown, or displayed in aroused state, or touching, it isn't classed as hardcore.
Such sites also do not show the actual sex, but it is clearly implied as to what will transpire.
That is also open to interpretation, as some 'softcore adult sites' will show some form of stimulation, some form of touching, but do not show the actual climax, hence their attempt to class themselves as 'softcore'
Magazines like Playboy are considered 'softcore' as they do not display sexual penetration. Magazines like AllBoy on the other hand do show a lot more, and are classed as 'hardcore' publications.
Noteworthy: An attempt is underway to add a new rating to movies, Hard R, which again is due to pressure from Religious Groups, protesting the sex and violence. Film studios and producers are objecting, as this could include many of the more extreme horror flicks that kids seem to thrive on.