The words people actually use
In ordinary speech a document is legalised, stamped, apostilled or certified, and the four are treated as a single idea. In practice they name different acts, performed by different bodies, with different effects. That looseness costs nothing on a route where one mark finishes the job, and it costs a great deal on a route where it does not.
Where Taiwan stands
Taiwan has not joined the Hague Apostille Convention. An apostille from United Kingdom to Taiwan is therefore a stage rather than a conclusion, and the file carries on to a consular desk after the British office has finished with it. The difference between the two words matters here precisely because both stages exist on this corridor.
Which body performs which act
Leicester Registration Service at 115 Charles Street, Leicester LE1 1FZ produces certified copies of locally registered civil entries — the word there is certified, and it means a faithful copy of a record. The FCDO Legalisation Office at PO Box 6255, Milton Keynes MK10 1XX then adds the British mark by post. Neither of those steps is what a request means by legalised.
The figure that gets quoted, and the one that does not
Prices follow the same confusion. A published British figure exists — £45 a document by standard post, £40 a document next-day for a registered business — and it is often repeated as though it were the price of the whole thing. It is the price of one stage. The consular charge is separate and belongs to a different body altogether.
Saying what you mean when you ask for it
The safest habit is to name the stage rather than the process. What you need for an apostille for Taiwan is one particular British certificate; a request for legalisation wants that certificate plus the consular mark that follows it. Using the narrow word for the narrow act keeps both halves visible, and it stops the question being answered with the wrong stage.