含义不同，用法不同。go on to do的含义是做了一件事后，接着做另一件事；go on doing的含义是继续做原来做的事。go on doing是分词作宾语；go on to do是不定式作目的状语。
go on to do的用法
go on to do sth的意思是：做完某事后接着做另一事。其中的不定式为目的状语。如：
He went on to show us how to do it.他接着又教我们如何做。
The minister went on to talk about foreign policy.部长接着就谈外交政策。
Go on to do the other exercises after you have finished this one.做完这个练习后，请接着做其它的练习。
After approving the agenda, we went on to discuss finance.通过了议事日程后，我们接着讨论财政问题。
He began by showing us where the island was and went on to tell us about its climate.他先给我们指出那个岛的位置，接着就讲起岛上的气候来。
go on doing的用法
go ondoing sth的意思是：继续(不停地)做正在做的事。如：
The minister went on talking for two hours.部长一连谈了两个小时。
You can’t go on working all night without a rest.你不能通宵工作而不休息。
We went on talking till after midnight.我们继续谈话直到午夜以后。
You can’t go on working without a break.人不能不停地工作而不休息。
You’ll crack up if you go on working so hard.你继续这样拼命干下去，身体会吃不消的。
to do和doing的短语
remember to do记得要去做某事；remember doing记得做过某事
forget to do忘记要去做某事；forget doing忘记做过某事
mean to do打算做某事；mean doing意味着
stop to do停下来去做另外一件事；stop doing停下正在做的事
regret to do遗憾地去做某事；regret doing后悔做过某事
try to do试着去做某事；try doing试着做了某事
like to do喜欢做某事（一次）；like doing一直喜欢做某事