That's why --- unless your purpose is limited to crossword puzzles --- definitions consisting of more than one word enable you to convey the meaningful differences between proselytism and evangelism, both in word and in practice.
It's like the difference between "cult," "faith," and "church".
Or "teach," "train," and "indoctrinate".
Or any number of similar words with different connotations in different contexts.
Until recently had Paul tried to preach publicly (proselytize) as he did in the forum he would have been arrested and jailed by Greek authorities at the behest of the Greek Orthodox Church.
“There are different connotations as well as legal distinctions in different countries.”
Of course there is and the connotations are false and an excuse to deny religious freedom to unpopular or minority religious groups.