A certified translation is the complete, accurate translation of your document together with a signed statement confirming it's complete and correct. Neither the US nor the UK operates a sworn-translator system, so what makes a translation acceptable isn't a court appointment or a government-issued title, it's whether the statement, the signature and the translator's credentials are there and verifiable.
In the US, USCIS requires the full English translation of every foreign-language document in an immigration filing, together with the translator's certification that the translation is complete and accurate and that they're competent to translate, plus a copy of the original attached. A certified translation USCIS caseworker will accept is one where that certification is genuine and verifiable, there's no official government list of approved translators. In the UK, the Home Office, in a joint statement issued with the UK's own professional bodies, specifies four things a certified translation must carry, a statement that it's a true and accurate translation of the original, the date, the translator's full name and signature, and their contact details. UK authorities also expect the translator or company to be traceable through a recognised professional body, the Institute of Translation and Interpreting (ITI), the Chartered Institute of Linguists (CIOL), or the Association of Translation Companies (ATC). PoliLingua is an accredited ATC member, which is exactly the credential UK caseworkers look for.
If you've been searching for certified translation UK requirements, you've likely come across the related terms certified translator UK, document translation services UK and notarised translation UK, all used loosely online for what the Home Office simply calls a certified translation, there's no separate formal category behind most of these labels. What some sites call sworn translation UK doesn't exist as an actual system in Britain either, sworn translation is a continental European mechanism, not a British one, so a UK caseworker reviewing a certified translation Home Office submission is checking for the four elements above, not a specific title. If you specifically need an ITI certified translation, note that PoliLingua holds ATC accreditation rather than ITI membership, both are recognised professional bodies under the Home Office's own joint statement, so either one satisfies the traceability requirement caseworkers look for.