The correct form is whichever is the statutorily prescribed or customary form for a particular court and particular jurisdiction; in other words, one should never write "court of appeal" when the court at issue clearly prefers to be called a "court of appeals", and vice versa.
ðə kɚɹˈɛkt fˈɔːɹm ɪz wɪtʃˈɛvɚɹ ɪz ðə stˈætʃətˌoːɹəli pɹɪskɹˈaɪbd ɔːɹ kˈʌstəmˌɛɹi fˈɔːɹm fɚɹə pɚtˈɪkjʊlɚ kˈoːɹt ænd pɚtˈɪkjʊlɚ dʒˌʊɹɹɪsdˈɪkʃən; ɪn ˈʌðɚ wˈɜːdz, wˈʌn ʃˌʊd nˈɛvɚ ɹˈaɪt "kˈoːɹt ʌv ɐpˈiːl" wˌɛn ðə kˈoːɹt æɾ ˈɪʃuː klˈɪɹli pɹɪfˈɜːz təbi kˈɔːld ˈeɪ "kˈoːɹt ʌv ɐpˈiːlz", ænd vˈaɪs vˈɜːsə.