Two stages, one shared word
Nigeria has not joined the Hague Apostille Convention, so a British mark alone does not answer for a paper used there. Papers going that way need embassy or consular legalisation instead: certification by the FCDO Legalisation Office, then a consular stamp on top of it. The same word sits in the name of the earlier body and in the description of the later one.
Where Nigeria stands
An apostille is not accepted for Nigeria, and knowing that is what makes the double meaning safe to handle. If the shorter road were open here, the two senses would rarely collide, because nothing would sit after the British stage at all. Something does sit after it, and that something is the part the destination actually cares about.
What the British office is and is not
The Legalisation Office is one central body, working by post rather than over a counter, and it certifies British documents for use abroad in general rather than for any single destination. Its name describes that broad job. It does not promise that a sheet leaving it is ready for a country whose rules put a consular act after it.
The consular stamp is a separate act by a separate body, and it is where the second sense of the word lives. Nothing in the British name reaches into it. Reading a returned envelope as the end of the story is the commonest way a Nigeria-bound file loses a month, and the wording on that envelope carries most of the blame.
Cost and timing across both senses
Only the earlier stage has a printed price: £45 for a document sent standard postal, £40 for one on the next-day rate open to registered businesses, counted sheet by sheet. The later stage carries a charge of its own and a pace of its own, fixed at the consular desk. The word may be shared between them; the price lists are not.