The Mirror is "not like other tabloids", which is both true and also its new advertising slogan. In one image from the campaign, launched last weekend to coincide with a "design refresh", the line runs below a picture of a cheery young woman in a bath with her elbows poking out over the sides.

The Mirror is branding itself as the red-top with a "brain" for readers with brains. There is a hashtag to support to exercise, #Madeuthink, as in #Madeuthink the bath model's sudsy elbows were bare breasts. They say people do see what they want to see.

The Mirror, according to editor Lloyd Embley, is "less about titillation and more about proper news", now presented in less brash fonts. His message is that it is not the Sun, which resolutely sticks to its Page Three cartoon. On Mirror.co.uk, Embley also mocks online publications by explaining its new #Madeuthink manifesto "for the digital generation... with added miaow" in a series of cat gifs. "We're the intelligent tabloid," says a bespectacled fluffy white feline.

"The Mirror has never been the Star or the Sun," says John Kierans, the Mirror's editor-in-chief in Ireland, who oversees its daily and Sunday editions in both the Republic and Northern Ireland.

Like the British edition, the Irish Mirror titles get a comparatively big sales uplift from "serious" news stories, Kierans says, citing the Boston bombings. Not that it ignores the celebrity drip-feed: it has also enjoyed good fortunes by splashing on the Simon Cowell baby saga. Politics "doesn't have the same gloss as the big international stories" but is important, and editorially the Irish Mirror treads a parallel political path to its UK counterpart.

It is Labour party conference week in Britain, and Ed Miliband's big speech has garnered headlines such as "Back to the bad old days" (Daily Mail), "Blackout threat over Miliband's fuel speech" (The Times) and "Red Ed power cut fear" (the Sun). The Mirror went for the more on-message "Ed: I'll freeze your gas and electric bills for 2 years".

Here, the Irish Mirror supported "Gilmore and co" in the Labour Party at the time of the last general election. "But there has been a lot of broken promises, so we have given them a kicking since then," says Kierans. "We passionately believed Labour could be a force for good in the country, and we think they still can be a force for good, but they have lost their way."

Since the Irish Sun's decision to move away from topless Page Three girls, the difference between the Mirror and its rivals highlighted in the bath advertisement has a smidgeon less relevance in this market.

But there is one other important way in which the Irish Mirror, regarded by some as the also-ran of British titles, is now distinguishing itself from its traditional competitors: it has invested in breaking news. In June, it launched IrishMirror.ie, hiring six online reporters to pump out locally flavoured content and creating what Kierans calls "a massive beast that has to be continually fed".

It may surprise some consumers already inundated with instant links to often quite generic news, but the Irish Mirror saw, and still sees, a gap in the market. "We very much see it as being between ourselves and the Indo," says Kierans. "The Star doesn't have what we have. They can dress it up all they like, but they don't. MailOnline, globally, is a fantastic product, but they don't do Irish breaking news."

Although a paid-for weekend app is in the pipeline, the Irish Mirror's e-edition, more interactive than most, "will remain free Monday to Friday", he adds. Indeed, Trinity Mirror's broad shunning of web paywalls – a commercial philosophy that prompted defecting columnist Tony Parsons to claim the paper was "dying" – has placed it on a diverging strategic path to long-term enemy the Sun (which now has both a paywall and Parsons on its books).

These days, however, competition comes from all sides: online-only publications, public service broadcasters, content farms and everything in-between. For the generation of readers that don’t buy tabloids or even consume them digitally, styling a brand as an “intelligent tabloid” may seem anachronistic.

Transport for London, meanwhile, felt the elbows in the Mirror's double-take bath advertisement rather too closely parodied the toplessness of other red-tops and banned it from running "sexual imagery" on the Underground. Indeed, some readers may, like TfL bosses, concur that it is not quite as easy to tell the Mirror apart from other tabloids as it would like to think.