There were four skill levels.
Ordinary
Instructed
Skilled
Competent
The latter had the safety of others in the title, for some reason a regular question on the BS 7671 exam. But Competent was dropped, it was a bit silly to have the two, but a competent persons scheme has nothing to do with being competent, it means you have met the criteria to become a member, and not been caught doing anything wrong, and you pay an annual fee.
It replaced the closed shop with the Unions, and data protection stops the different scheme providers swapping info, so if you get thrown out of one, you can join another, and there must be at least two scheme providers or it would be a closed shop, and firms can't demand you are a member of any one of the scheme providers as again that would be a closed shop which is illegal.
There is also the LABC who can also over see who does electrical work, as with the scheme providers they must ensure the guy has the skill required, but as a job to job basis, not a blanket cover of all jobs of the type agreed.
Many scheme members can't do all electrical work under the scheme, often the electrical installation condition report (EICR) is not covered by the scheme membership, and scheme members only can use the scheme providers logos, so if an electrician displays the scheme providers logo anywhere, then he is responsible for ensuring all work requiring registering is registered. Other wise it is down to the home owner.
The English parliament set the rules, then gave devolution so Wales can set it's own rules, then relaxed the rules, but the Welsh did not follow suit, Scotland has had its own rules since they started.
In theory the records are kept, but when I tried to get replacements it became apparent it is a deterrent and a tax only. I have seen court cases where the work was sub standard, and where electricians claimed to be scheme member but were not, but not any due to simply not registering the work.
In Wales if I use an extension lead in a kitchen and put some cleats to keep cable tidy, i.e. fix the cable or socket to the wall, even if plugged in, it needs notifying, I would not think anyone would do that, a little common sense is required.