Ask sb to do表示要求某人做某事，用动词不定式表示；而Ask sb doing表示询问某人正在进行的动作或情况，用动词的进行时形式表示。Ask sb to do常用于请求、指示或邀请等正式场合；Ask sb doing常用于询问、交流等非正式场合。它们在释义、用法、使用环境、影响范围和形象上存在一些区别，具体内容如下所示。
1. 释义区别
Ask sb to do要求某人做某事。Ask sb doing询问某人正在做某事。
例句
I asked my friend to help me move to a new apartment.（我请朋友帮我搬到新公寓。）
I asked him what he was doing in the park.（我问他在公园里做什么。）
2. 语法区别
Ask sb to do通过动词不定式来表达要求。Ask sb doing通过动词的进行时形式来表达询问。
例句
He asked her to meet him at the coffee shop.（他要求她在咖啡店见面。）
She asked me what I was doing over the weekend.（她问我周末在做什么。）
3. 用法区别
Ask sb to do表示请求、指示或邀请某人做某事。Ask sb doing表示询问某人正在进行的动作或情况。
例句
The teacher asked the students to finish their homework by tomorrow.（老师要求学生们明天前完成作业。）
I asked my friend what he was doing for his summer vacation.（我问朋友他暑假在做什么。）
4. 使用环境区别
Ask sb to do常用于请求、指示、邀请等正式场合。Ask sb doing常用于询问、交流等非正式场合。
例句
The manager asked the employees to submit their reports by the end of the day.（经理要求员工们在今天结束前提交报告。）
I saw my neighbor in the garden and asked her what she was doing.（我在花园里见到邻居，问她在干什么。）