Extreme sexual depictions which includes 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.
Any depiction where one or more persons are naked, and the viewer can see their genitals, in a fully aroused state.
In addition, it includes touching, or other actions that would elicit a sexual response from the viewer.
The act of penetration, in some form is generally considered to be 'hardcore' even though the genitals may not be shown fully aroused.
Penetration, whether by finger, toys, or penis, is considered to be the main defining criteria on whether the material is hardcore or not.
Practice (Associated Acts): A more advanced form of hardcore, in that the acts displayed, or depicted are not what one considers standard fare.
This mostly would apply to BDSM type of depictions, where the acts appear to border on being illegal or not.
Bondage scenes for example can resemble rape scenes, thus coming close to crossing some legal thresholds. Even though consensual, there are communities where such acts are just not allowed.
Much of SandM would be fall under the 'extreme' label, due to its nature of inflicting of pain.
Furries on the other hand, could easily fall under the 'softcore' category, as it is more about the dress, than the sex.
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.
Hardcore has been used in other ways, to denote something, or someone, that is very complex, very detailed or involved. For example, someone can be called being a hardcore fan of a group, or a game, meaning they are very devote, very determined.
Hardcore Religious Nut, Follower or Fanatic is another phrase using 'hardcore' to establish a deep sense of belief, involvement which is considered beyond the normal.