You use certainly to emphasize that what you say is definitely true. His death was certainly not an accident. You use surely to express disagreement or surprise. Surely you care about what happens to her. Both British and American speakers use certainly to agree with requests and statements. 'It is still a difficult world for women.' —'Oh, certainly.' Note that American speakers also use surely in this way. 'Can I have a drink?' —'Why, surely.'

certainly可以用来强调所说内容属实：His death was certainly not an accident (他的死绝非意外)。surely 可用来表示反对或惊讶：Surely you care about what happens to her (不用说，你一定关心她的事吧)。美国人和英国人都用 certainly 表示同意请求和陈述：‘It is still a difficult world for women.’—‘Oh, certainly.’(“如今的世界对女性而言仍然很不容易。”—“嗯，那当然。”)注意，在这种情况下，美国人也用 surely: ‘Can I have a drink?’—‘Why, surely.’(“我能不能来杯饮料？”—“噢，没问题。”）