The narrow claim on the certificate
An apostille is a printed slip fastened to your paper. It names the official who signed below it, gives the post that person held, and confirms the seal beside the name. It does not read your sentences, test whether they are correct, or ask what you mean to do with them. Its claim is narrow on purpose.
That narrowness is what makes the treaty work at all. A clerk in Ulaanbaatar has no way of knowing how a Welsh registrar signs, or what a British court seal looks like. The slip answers that one question for them, in a form every member country has agreed to read, and the rest of the file stays theirs to judge.
Mongolia inside the Convention since 2009
Mongolia joined the Hague Convention in 2009. Once two countries sit inside the same treaty, each takes the other's certificates as they stand, and nobody has to walk a file round an embassy first. So an apostille from United Kingdom to Mongolia is the finished article: one slip, fastened in Britain, read on arrival.
Getting a sheet the office can mark
Because the mark fastens to a signature, the sheet you send has to carry one. Cardiff Register Office at City Hall, Cathays Park reissues birth, marriage and death records as certified copies, each signed in the usual way, and a copy from there is marked exactly as an older certificate would be.
The marking itself happens at the FCDO Legalisation Office in Milton Keynes. That office works entirely by post, so there is no counter in Wales to walk into and no slot to book. The charge is fixed per document, which turns the size of your bundle into the only real cost decision you make.
Three things the slip will not fix
It will not correct an error already printed on your document. A misspelt surname or a wrong date stays as it is, and the slip then proves only that a real registrar signed the misprint. It will not turn your words into another language. And it will not make a paper nobody asked for suddenly count, so start from the list you were given rather than from the folder you already keep.