Near the entrance to the exhibition, a medium-sized image depicts a Japanese woman in loose, sensuous clothing that parts to reveal a cheeky flash of pale leg. Other paintings leave less to the imagination; they are replete with pubic hair and sex toys and gravitationally implausible scenes of coitus. One shows a nun with a shaved head having sex with a priest who is hidden in a large bag. Another shows a group of men engaged in a "phallic competition", their gigantic, exaggerated penises resting on tables and kickstands. A third shows a woman being pleasured by two octopuses.

If these were photographs, they would be hidden away on the top shelf at some seedy corner store. Instead, they are paintings – and they are on display at London's esteemed British Museum. Visitors under 16 years old must be accompanied by an adult. What's certain is that this ongoing exhibition Shunga: Sex and Pleasure in Japanese Art raises important questions about the juncture between art and free speech, some of which are unique to our digital age.

"Shunga", which translates to "spring pictures," was a popular Japanese painting style for hundreds of years. In the words of the exhibition curator Timothy Clark, Shunga "celebrates the pleasures of lovemaking, in beautiful pictures that present mutual attraction and sexual desire as natural and unaffected." Often, Shunga paintings are humorous; sometimes, they are subversive – gently poking fun at the cultural and aesthetic mores of their time.

Though officially banned by the Japanese government in 1722, Shunga continued to be produced – and was often commissioned by wealthy patrons. Shunga paintings were passed around through lending libraries, or gifted to lovers and spouses. They were also used as sex education for newly married couples. The paintings are certainly explicit. And erotic. But are they also pornography, which might place legal limits on their distribution and audience? If they are pornography, could they be considered obscene – a point of legal importance?

British law is hazy on the question of obscenity; following a landmark judicial ruling, pornographic material is considered "obscene" if it has "a tendency to deprave and corrupt" its audience. Some organisations, like Britain's Campaign Against Censorship, have called for the creation of a statutory defense of "artistic merit", which artists could rely on if accused of obscenity. As to the issue of 'art' versus 'pornography,' one might recall the American Supreme Court Justice Potter Stewart who, in 1964, famously declared, of pornography, "I know it when I see it."

Assuming that we should be able to formulate a more coherent definition, let us break the question down: does it matter that these are paintings – as opposed to photographs? Or: does the fact that these are paintings immediately imply that Shunga is art, rather than pornography? This seems an overly simplified distinction, especially in the digital age: when Photoshop and digital editing can turn once-"real" images into artistic fiction – and graphic design tools can build realistic-looking pictures from digital scratch. Does artist's intent matter? Does provenance? Some who are eager to locate the art/porn fault line stress the importance of artist's intent. If an image is meant to elicit arousal, it's porn; if not, it is art. Others look to provenance. Were the images produced by an artist or an amateur? Were they commissioned by a gallery, or thrown up on Facebook?

This method also seems flawed – not least because we can't always know an artist's intent, and because what is arousing to one person can be horror-inducing to the next. That would, by extension, mean that something can be art when viewed by one person and porn when viewed by another. Furthermore, a focus on provenance and intent leaves the art/porn categorisation up to gallery owners and curators and other institutional "authorities" – who are unlikely to agree anyway. Besides, Shunga was meant both to arouse and to educate. So where would it fall? Is the definition fluid … a product of place and time?

Shunga first made its way to England in the early 1600s, via the English East India Company – but when the photos surfaced in London, outraged company officials set them ablaze. In Europe, explains Shunga curator Clark, "since at least the Renaissance … prevailing religious and social bans have made it well-nigh impossible for leading artists to produce works that are explicitly erotic."

If we allow that morality and aesthetics are both shaped by culture, and not universal and constant, than is it possible that Shunga can be at once art in Japan and porn in England?

I am, oddly enough, reminded of an interview with Cooper Hefner, the 21-year-old son of Playboy founder Hugh Hefner. Playboy is art, not porn, the younger Hefner recently insisted: "If you consider Playboy pornography, then you consider any photo of a nude woman or man pornography." Is it possible that Hefner Jr hit on a valid point? Playboy was brash and bold and wholly pornographic in its time; but today its still shots of topless blonds seem rather quaint. Is it possible that the same image was porn in the 1950s and is art today? Taken further, could it be that there exists some fuzzy line (say, around "orgy" or "fellatio" or "sex toy") beyond which erotic art becomes porn? And does that line move? Does intensity of the subject matter?

What's notable about Shunga is that all its subjects – men and women (not to mention octopi) – seem to equally enjoy their sexual adventures. In this way, Shunga appears incredibly progressive for its time. Women enjoying sex! And, sometimes, with each other! This progressiveness makes the exhibit all the more palatable to today's audience. But let's imagine a different scenario. What if the drawings depicted children engaged in sexual acts? Or rape? Or subjects expressing pain and fear? Would that change things? Would those images be enough to incite "depravity"? Would and should that lead us to place restrictions on who can view the paintings?

The state of the game seems to be this: producers and curators decide what is art and what is porn, what is erotic, and what is obscene. Unsatisfactorily, it's plausible that Shunga is art precisely because it is displayed on the walls of the British Museum. In general, the very idea that there exists a line between "art" and "porn", between "art" and "obscenity", seems inherently flawed. "In the west, we have created a state of affairs where there has to be a firewall between art and pornography," muses curator Clark. "But Shunga is both sexually explicit and demonstrably art."

• Shunga: Sex and Pleasure in Japanese Art continues at the British Museum, London until 5 January 2014