Accomplishment и Achievement... В чем разница между этими двумя английскими глаголами

Это существительные.

Accomplishment - это "достижение" в смысле "выполнение", "завершение", "осуществление"
Achievement - это "достижение" в смысле "успех", "подвиг"

to achieve – an achievement | to accomplish – an accomplishment | accomplished

Achievement - это "достижение" в смысле "успех", "подвиг", «достигнуть цели».

Anybody will do his best to achieve this goal. Стараться, что бы достигнуть
We achieved what we set out to do. Мы достигли того, что намеривались сделать.
That year they achieved their independence. Они добились…
His words achieved their object. Его слова достигли своей цели
He thinks his talent and achievements annoyed a lot of people. Его талант и достижения…
His crowning achievement is this baby of his. Наивысшее достижение
It was a great achievement that a month later a global agreement was reached. Огромное достижение.

Accomplishment - это "достижение" в смысле "выполнение работы", "завершение проекта", "осуществление".

He has accomplished his promise by shooting himself in the throat. Выполнил свое обещание…
He accomplished 50 years. Он достиг 50 летия.
The work of the reformer was never accomplished so long as anything remained to reform. Никогда не завершалась, выполнялась, достигалась.
These qualities of her go to accomplish a perfect woman. завершают
I wish you success in the accomplishment of your important mission.
It was a real accomplishment to defeat them.
Your dad is a man of many accomplishments. Твой отец это человек, который многого достиг.
Every accomplishment starts with the decision to try.
He's an accomplished power forward who knows how to score a goal. Опытный, подготовленный, завершенный

Achievement - это "достижение" в смысле "успех", "подвиг", «достигнуть цели».