Actually it seems from several of your examples they are being distinguished from each other
Wouldn't it be redundant to use both words connected with the conjunction "and" if they meant the same thing?
Also the first one is probably more properly "teaching and evangelizing"..
euaggelízō; fut. euaggelísō, aor. euēggélisa, from euággelos (n.f.), bringing good news, which is from eu (G2095), good, well, and aggéllō (n.f.), to proclaim, tell. To evangelize, proclaim the good news, preach the gospel.
It was at the time that the first Christians were "scattered abroad, and went about preaching the Word" after the martyrdom of Stephen (he being one of the seven), that the verb euaggelízō (G2097), to publish the good tidings or good news, was used by Luke in
Act_8:4,
Act_8:12,
Act_8:25,
Act_8:35,
Act_8:40. Used in the act. voice meaning to declare, proclaim (
Rev_10:7;
Rev_14:6); in the pass. voice, euaggelízomai, of matters to be proclaimed as glad tidings (
Luk_16:16;
Gal_1:11; 1Pe_1:25); of persons to whom the proclamation is made (
Mat_11:5;
Luk_7:22;
Heb_4:2,
Heb_4:6; 1Pe_4:6); in the mid. voice especially of the message of salvation with a personal obj., either of the person preached (
Act_5:42;
Act_11:20;
Gal_1:16), or with a prep., of persons evangelized (
Act_8:12;
Act_13:32;
Eph_3:8).
Not found in Gospel of Mark, or the epistles and Gospel of John, only once in the Gospel of Matthew, and twice in the Book of the Revelation. Related to euaggélion (G2098), a good message. Also from euággelos (n.f.): euaggélion (G2098), good news.
Zodhaites