Affray is more a threat of breach of the peace, though it may involve the actual breach. Some years ago I was on a jury hearing an affray and we were given a printed out definition to ponder before the trial got under way. The bit that amused me was “conduct is such as would cause a person of reasonable firmness present at the scene to fear for his personal safety.” wikipedia covers it reasonably well.
Affray is usually dealt with at the level of magistrates court, the lower level in England and Wales, which deals with about 90% of what comes before the courts. If the affray came before a court the “admission” will have been a guilty plea and possibly an admission to the police beforehand to save them having to collect evidence and build a case. Some come before a Crown Court if they’re more serious or the defendant thinks they stand a good chance with a jury. You’d only do that if you were pleading not guilty.
There is another way that less serious offences are sometimes dealt with. If a person admits guilt they may be offered a police caution. While not the same as a conviction it is nevertheless a serious matter, and only happens when guilt is admitted. https://en.wikipedia.org/wiki/Police_caution. This would, I suppose constitute an admission.
Whether an affray would be dealt with by way of a caution, I don’t know. But these are two ways that admitting affray might happen in the English legal system.
The difference between a barrister and a solicitor has traditionally been that of advocacy. A barrister is a lawyer who is permitted to stand up for you in court. The regulations have been relaxed in recent years and solicitors are now allowed to do advocacy work in the lower courts. Solicitors do a lot of legal work like wills, conveyancing and drawing up contracts that barristers for the most part don’t. If those wills, conveyances and contracts come to court you’ll be needing a barrister but a solicitor will do most of the legwork preparing the case.
In the case of our affray, if you’re offered a caution, it’ll most likely be a solicitor who advises you whether or not to accept it. If it gets as far as a magistrates court a solicitor may represent you. If it goes to crown court you’re going to be instructing a barrister but again, a solicitor will be doing the legwork. I’m not a lawyer, so don’t take this as gospel.