"To continue doing something" 和 "To carry on doing something" 都可以表示“继续做某事”的意思。
"To continue" 来源于拉丁语 "continuare"，意思是“连续不断地做”。
"To carry on" 来源于中世纪英语 "carien on"，意思是“继续进行”。
例句1:
"I'll continue working on this project until it's finished."
(我会继续工作在这个项目上直到完成。)
例句2:
"Let's carry on with the meeting even though he's not here."
(让我们继续开会尽管他不在这里。)