Three words, three different acts
A certified copy is the first of the three. It is a fresh official print of a record, made by the office that holds the original entry, and it exists so your own sheet never has to travel. Nothing about it is aimed at another country. It is simply a safe substitute for the paper you would otherwise put at risk in the post.
The second is the apostille: a fixed-form certificate joined to a sheet, which speaks for the signature and seal already on it. The third is legalisation, a chain in which several desks each add a mark in turn. All three end with an official stamp, which is why people swap the words, but they are not the same act and they do not cost the same.
Which of the three applies here
Libya has not joined the Hague Apostille Convention, so the second word is out. There is no apostille issued in Leicester for use in Libya that will finish a file, and there is no faster tier or special case that turns one into a finished job. Document legalisation for Libya is the third road: a chain of stamps rather than a single certificate.
That leaves the first and third words in play. You will still want a certified copy, because the record has to exist in a form that can safely travel, and then the chain runs on top of it. An apostille for Libya sits outside both of those steps and adds nothing to either.
What the confusion actually costs
Searches for what you need for an apostille for Libya are common, and the phrasing is understandable, but acting on it without checking the shape of the route wastes real weeks. There is no apostille from United Kingdom to Libya that a receiving desk treats as complete, so a run made on that assumption ends with a stamped sheet and an unfinished job.
The loss is mostly time, and time on a chain route is the expensive currency. Each stage has to finish before the next can begin, so a fortnight spent on the wrong word does not overlap with anything; it simply pushes the whole run back by a fortnight. Getting the vocabulary straight is the cheapest correction available.
What the words mean at this end
In practice the first word has an address. Leicester Registration Service, at 115 Charles Street, Leicester LE1 1FZ, prints certified copies of civil records held locally, and a copy from there travels in place of the sheet you keep at home. That is a plain, cheap act with no foreign element to it at all.
The other two belong to central offices rather than local ones. The FCDO Legalisation Office at PO Box 6255, Milton Keynes MK10 1XX is a government office, not one of ours, and it works by post with no counter for callers. Beyond it the chain continues at consular level, which is where this corridor differs from a one-stamp route.