Normal people don't keep writing racist tweets before and after the Southport murders & during the following riot, Connelly did, she wrote many such tweets, over many months... this wasn't an isolated incident.
From the CPS
“The prosecution case included evidence which showed that racist tweets were sent out from Mrs Connolly’s X account both in the weeks and months before the Southport attacks – as well as in the days after
Messages to friends show that she planned to use her children to escape justice, but such was the overwhelming evidence, she pleaded guilty.
I suspect that had Connelly written just one such tweet, she would have been advised very differently.
Jones had a jury trial, for him to be found guilty the threshold of "Beyond reasonable doubt" has to be reached... in this case 12 ordinary people found him Not Guilty
As for having "the book thrown at her" the evidence is that she wrote that book herself.