The answer would depend on the specific person.

But if I have to make a guess, I would say that internet is also real world. The people behind the post and writings are real people. The things that are written affect real world. From publicity to ideas. There are plenty of studies that show that FB influenced real elections. Millions of dollars/euros invested on those platforms in order to lobby for some laws that, in the end, affect real world.

Also, online harassment can be very real and used to affect people outside the net. For example, social networks used against women with very real life threats or even encouraging people to use tactics as false denounces so policie show in the house of the victim under false pretenses. Also there is revenge porn. I could go on.

Point is, the same way that some people use linkedin to get a job (another very real effect outside the net), some people use it to harm others. People who felt strongly about a “simple response” on twitter other social network, might very well suffer the effects of such hateful comments. For that person both things are related.

As a very simple example, the far right political party VOX (spain) wasn’t a surprise for the people who complained about misogyny on the net. And there is already a rise on deaths from domestic violence derived from the cuts in prevention those parties are enforcing.

I would like to think that people who said hateful things are “just trolls” or “just joking”, but the results aren’t as easily ignored.

Words are never “just words”. Internet and any other media, just like books, are used to transmit ideas and ideas shape the world. That is why some people burned books, or want to censor internet (china and probably more countries). Information is power, but as we learned from second world war, propaganda works as well.