Both theories easily describe the first reaction: CH3COOH acts as an Arrhenius acid because it acts as a source of H3O+ when dissolved in water, and it acts as a Brønsted acid by donating a proton to water.
bˈoʊθ θˈiəɹiz ˈiːzili dᵻskɹˈaɪb ðə fˈɜːst ɹɪˈækʃən: sˌiːˈeɪtʃ θɹˈiː kˈuː ˈækts æz ɐn ɚrhˈiːnɪəs ˈæsɪd bɪkˈʌz ɪɾ ˈækts æz ɐ sˈoːɹs ʌv ˈeɪtʃ θɹˈiː ˈoʊ plˈʌs wɛn dɪsˈɑːlvd ɪn wˈɔːɾɚ, ænd ɪɾ ˈækts æz ɐ bɹˈɑːnstᵻd ˈæsɪd baɪ doʊnˈeɪɾɪŋ ɐ pɹˈoʊtɑːn tə wˈɔːɾɚ.