1.要表示：相一致；符合；相符, correspond to和correspond with都可以用：
Your account of events does not correspond with hers.
你对事情的陈述与她说的不相符。
The written record of the conversation doesn't correspond to what was actually said.
那次谈话的文字记录与原话不符。
Racegoers will be given a number which will correspond to a horse running in a race.
观看赛马比赛的观众将获得一个与某一匹赛马相对应的号码。
Give each picture a number corresponding to its position on the page.
按所在页面位置给每一幅画编上相对应的号码。
The marks correspond to points on the map.
这些标记与地图上的各点相对应。
That corresponds to /with what he told me.
这与他说的话是一致的。
These goods don't correspond with ( to) the list of those I ordered.
这些货物与我的订货单不相符。
This copy does not correspond with the original.
这份副本与原件不符。
The translation does not quite correspond to the original.
译文不切原意。
Her expenses do not correspond to his income.
她的花销与他的收入不相称。
2. correspond to sth,还可以表示：类似于；相当于，同义词 equivalent：
The British job of Lecturer corresponds roughly to the US Associate Professor.
英国的讲师职位大致相当于美国的副教授。
The working of this machine corresponds to that of the human brain.
这种机器的作用就相当于人脑的作用。
The American Congress corresponds to the British parliament.
美国的国会相当于英国的议会。
3. correspond with sb还可以表示：与……通信
She still corresponds with American friends she met in Majorca nine years ago...
她仍与9年前在马略卡岛结识的美国朋友们通信。
He often corresponds with his friends.
他常和朋友们通信。
Janet and Bob corresponded with each other for many years.
珍妮特同鲍勃许多年来一直互相通信。