Why this route has two desks
Burkina Faso has not joined the Hague Apostille Convention, so a British mark by itself does not settle a paper used there. Records bound for it need embassy or consular legalisation instead: certification by the FCDO Legalisation Office, then a consular stamp placed on top. Two desks, one after the other, and neither of them a proofreader.
Where Burkina Faso stands
An apostille is not accepted for Burkina Faso, and no amount of care over the paperwork alters that. It is worth being blunt, because from the outside the two roads look much the same — an envelope, a charge, a wait, a sheet coming back with something official on it. The real difference lies in where the finished sheet is read and who reads it.
What each desk actually looks at
Certification of this kind speaks to the signature and the seal on the sheet — who signed, and in what office — rather than to what the sheet says. That is a narrow job, and narrow on purpose. It tells the reader at the far end nothing whatever about whether the name on your certificate is spelt the way you spell it.
The consular stamp is the destination's own act and it comes second. It, too, goes on the sheet rather than into it. So the record you send is the record that arrives, errors and all, having picked up two marks along the way that say nothing about its contents.
The price of finding out late
The British charge is published and counted sheet by sheet, and the consular charge sits outside it, set somewhere else entirely. Both fall due again if the record has to be replaced and sent round a second time. That is the whole argument for ten slow minutes with the certificate on the table before any of it begins.