And now over to Lucian with the nudes

The Naked Portrait Compton Verney, Warwickshire, until 9 Dec

Walter Sickert: The Camden Town Nudes Courtauld Gallery, London WC2, until 20 Jan

The naked truth, the naked ape - we never talk of them as nude, just as we don't go nude into the conference chamber. That is because naked means stripped bare, exposed, helplessly or forcibly revealed, whereas nude implies something more carefree or defiant. A baby is naked because it is innocent of volition; a woman is nude when she slips off her clothes. Nude is assertive, nude is purposeful, nude has nothing to hide.

And as in life, so in art. Take two examples from The Naked Portrait, an enthralling show. Bert Stern's famous photographs of Marilyn Monroe, taken just before she died, show her unclothed behind a diaphanous veil. But she is not an anonymous model, posing naked as required, she is Marilyn appearing in the nude - or rather Marilyn clothed, of course, in her own luminous beauty.

The girl in Lucian Freud's Small Naked Portrait, by contrast, is precisely naked: a poor, bare forked animal with bruises and freckles and reddened hands laid on a bed with nowhere to hide. She may even be trying to shield herself with one arm from the artist's all-seeing eyes. And this nakedness is her central condition to Freud. He looks at, and he paints, her face with the same degree of interest as the sole of her foot. His eye travels over her living figure, top to toe, as if it were all of equal importance, as if she were a landscape, or, less generously, a corpse.

We know the difference between naked and nude but what happens when they apply to portraits? Can Freud's painting even be described as a portrait at all? A great aspect of this exhibition of a hundred or so images is that it puts both nudity and portraiture to the test. Is there such a thing as a nude portrait? Is there an artist who can paint a person naked (as opposed to nude) at their own request?

Ivan Massow, just to take a sensational case, commissioned Jonathan Yeo to paint him undressed before and after losing three stones in weight. Sure enough, Massow goes from slightly pudgy to being a fine figure of a man, although Yeo, super-smooth portraitist to the stars, paints him just as politely in both cases. But with one subtle shift - having Massow turn sideways and glance sharply back at us in the second painting - he throws the emphasis from haplessly naked to proudly nude.

Why would anyone want to be depicted without their clothes? Artists did it all the time in the 20th century, and for very different reasons: Egon Schiele to show himself as an emaciated martyr, Edvard Munch as a naked soul in hell, Robert Mapplethorpe as a saucy devil. A long line of women, well represented here, have done it to raise consciousness: Jo Spence and Hannah Wilkie as witnesses to cancer, Alice Neel flaunting old age, Jemima Stehli giving you an eyeful in return as she performs a worrying striptease.

One of the most shattering paintings, from 1920, shows the Scottish artist Cecile Walton naked after the birth of her second child. It is extremely hard to read the tone of it - cold exhaustion and a kind of daze in the mother's face, the body just a vessel the nurse is briskly washing. And how new the picture, too, must have seemed in its day: revolutionary for 1920.

For the naked portrait is mainly a 20th-century phenomenon. There are plenty of naked people in the art of the past, and we may even know their names. But nobody thinks of Botticelli's Venus as a portrait of Simonetta Vespucci or Manet's Olympia as a portrait of Victorine Meurent. Voltaire was sculpted bare (though not by choice); Charles James Fox is exposed almost to the waist in his portly bust. And there are others who wished to appear as embodiments of the naked truth, particularly during the Enlightenment.

But Bacon's lovers naked and harrowed, Stanley Spencer popping up like a little glove puppet beside his vast bare wife, Bonnard shirtless and decrepit in his bathroom mirror - this is truly modern art. And what it shows is just how uncommon the naked - and not the nude - portrait is. Spencer's meagre self, like a featherless bird, is a portrait; a shot of Linford Christie, his body a gleaming prototype, is no such thing.

And looking at the so-called Camden Town Nudes of Walter Sickert, one senses that the idea of the nude itself was in question at the turn of that century. In these dark and knotted paintings the figures of women lie undressed on beds, awake or sleeping but always with their faces averted and the viewer positioned as though watching or inspecting. You see them and yet you don't know them.

They are not nudes - or portraits - because Sickert doesn't allow you to view them that way. The artist is still in charge, whereas in The Naked Portrait, you see a certain reversal. The actor Erwin Osen turns himself into a skeletal marionette (very aptly) for Schiele. Madonna presents herself (very foolishly) as Olympia to Peter Howson.

Nudity becomes a performance, sometimes erotic; nakedness rarely does. And it is a strange fact of this show that although it provokes many of the responses we might have in life - curiosity, empathy, embarrassment, admiration - attraction is rarely among them. For naked people in portraits have to make themselves known by unusual and arresting means. By resisting the fact of nakedness, like plucky old Alice Neel, by gloating over it like Gilbert and George, by turning themselves back into babies like John Lennon huddling up to Yoko Ono. Identity emerges without clothes, and sometimes even without faces. Whatever we are as human beings, we are infinitely more than our bodies.