When I started posting on GYE and then shortly afterwards joined SA, I desperately wanted to stop masturbating and to stop looking at pornography. I knew that sexual lust was a problem, but I was not especially concerned with it as a problem in its own right. If I could just get away from the pornography and masturbation, "dayeinu"!!!! That would have been fine for me.
My attitude was, that when I start working to become as great as the Chofetz Chaim then I'll worry about lust, but in the meantime I have more serious worries (like not transgressing the Shulchan Aruch).
When I joined SA, I heard a lot about the addiction being lust and I started to use the phrase myself, but it took weeks until it sunk in. The pornography and masturbation are only symptoms, the problem and the addiction were actually to sexual lust. The program I got from my SA sponsor is the program of the Big Book, but simply substituting the word "lust" for alcohol. Lust is a form of sex that is often as powerful - if not more powerful, than physical sexual acts.
That's how I personally understand the Gemara in Brochos that "kosho hihurei aveiro yoser meiaveiro atzmo - the thoughts of sin are worse than sin". For anyone (addict and non-addict alike) sexually lustful thoughts are more toxic than sexual acts.
In a letter that SA founder Roy K wrote to Australian SA, he pointed out that in order to even qualify for membership in SA, just as alcoholics must have a desire to abstain from alcohol to belong to AA, so for SA there is a requirement for a desire to stop lusting in order to belong. Therefore, Roy wrote, those who just want to stop sex outside marriage or even masturbation, but they have no interest in stopping lusting, do not even qualify for membership in SA.
I am personally very grateful for this major stress on the "lust addiction" because I personally believe that I would never have been free of my addiction if I had limited my focus to sexual acts and ignored sexual lust, and I believe that I would not have had any meaningful recovery at all.