It doesn't: "Social isolation, a related condition, is different — it’s an objective measure of how few relationships a person has. The experience of loneliness has to be self-reported"
It states that yes; ironically, it also uses them interchangeably multiple times throughout the article.
But I also know people who do silly things when facing the fear of being alone. For them, perhaps being alone equals to loneliness. For sure, it makes them suffer.
Most psychologists will tell you "we're very social creatures" but I was VERY social for so long that now it just feels like a waste of my time. People are quick to throw their problems on everyone around them, I get tired of the neediness, the games people play, the ego trips, all of it. It's sort of like a been there, done that, not interested anymore.