Generally speaking, the letter "ч" is pronounced as "ch", shch as the words "чай" (chay, tea), "человек" (Chelovek, man.
However, in some cases, the letters "ч" and "щ" will change. When the letter "ч" is followed by "иы" or "ы", the pronunciation will become "щ", for example, чашкаач in the word "чакаа" (Chashka, teacup). And the word "мечи" (Maggie, Jian) is also pronounced as "shch".
In a word, the letters ч and щ in Russian have different pronunciations, but their pronunciation rules can be learned and memorized.