I got caught up in the aftermath of an incident where a man murdered his wife, seriously wounded her son then took himself a few miles up the motorway to finish himself off in front of a passing lorry. The full closure of the motorway for the police to investigate brought the region to gridlock for many hours. Tens of thousands of people were affected in a temporary way by the incident (plus the trauma to the families of his victims and witnesses). It didn't make it beyond the local media, other than national transport news as an incident causing a road closure.
There is a difference in motive, "lone wolf" or actively part of a wider network, there is a difference in someone allying themselves with a global cause to an isolated murder. The fact that organisations such as ISIS or Al Quada exist does affect security assessments, what we can bring through an airport, whether we arm our police etc.
Censorship would be counterproductive and lead to more speculation which would lead to more fear. The whole point of terrorism is to terrify people into submission.
Relatively speaking Wednesday's events were a damp squib in the league of terrorist attacks. That's ABSOLUTELY NOT said to undermine the impact of the deaths and injuries of the victims, rather that potentially, there could have been so many more to suffer the consequences. The incident was dealt with quickly and contained before higher profile targets could be attacked. People showed the best side of human nature, assisting others, getting people out of the way of ham.
It was a rich day for the media. Eyewitnesses included articulate MPs and journalists. People had phones out for sightseeing so the attack was recorded. As Wednesday afternoon and evening unfolded, there was more broadcastable material that could be used before looping.
What matters more is the long term reaction. There do need to be police/ security reviews as a routine course of action. Practical life in London was near normal the next morning. Most people accept that there is a risk of terrorist activity, but it's more worthwhile checking the road thoroughly before crossing. That's where this particular terrorist threat fails, because life goes on unchanged for the masses.