Richard, можно is a verb. it is used roughly as the verb "may" in English. "Можно войти?" — “May I come in?”, “Сегодня тебе можно съесть печенье” - "You may eat a cookie today".
while "мочь" is mostly used as "to be able to"

sorry, my bad. it's not a verb. it's called предикатив.
https://en.m.wikipedia.org/wiki/Predicative_expression

https://ru.m.wikipedia.org/wiki/Предикатив