The Public Order Act requires the use or threat of violence such that a notional person of reasonable firmness would be in fear for their safety.
Thereafter it's mostly about numbers: 12 or more for Riot; 3 for Violent Disorder; otherwise Affray.
Riot also needs a 'Common Purpose'.
Anyone charged will likely be for Violent Disorder. Easier to prove.
A relative of mine was literally* 'read the Riot Act', failed to comply and was transported to Australia.
* and I mean literally in the sense of literally, rather than the now more common, literally in the sense of figuratively
That would be the 1714 Act. I remember it well.* And as you say it involved a literal reading to those intent on going about their rioty business.
Interestingly, the Public Order Act retained the requirement of 12 or more. I don't know the reason for that number, then or now, but i suppose it just felt substantial enough to elevate it above the more mundane Saturday night Violent Disorder.
*only repealed in 1973 so it had a good innings.