Difference in what you can do with it
We take activities of LULZ/Anon etc with a pinch of salt because we all now that ultimately they are a bunch of bored teenagers. And it's kind of fun (sometimes) to watch bored teenagers do some mild mischief.
News Int however are grown-ups who wield a degree of very real power. When their activities overstep an invisible point of public disgust, we have a scandal, a reaction, some minor shuffling at the top, or if proven-illegalities, some jail time.
I doubt that Murdoch actually told his senior staff to break-the-law-to-sell-papers, but more likely created a highly-competitive culture with aspects of fear-driven success. Human ingenuity and flexible morality does the rest.
And whilst a large proportion of the voting public happily believe what they read in the papers without engaging their brain, then our elected representatives will continue to attempt to court those that write the words.
What is amusing/sad/overwhelmingly-wrong is that the disgust of the public is narrowed to focus on billionaires and politicians, rather than to reflect that it is their own lack of desire to think that allows/funds NI's corruption.