to teach english is her job/teaching english is her job??

两句都对
在这里没有区别 但不能一概而论 还是要根据当时的具体语境来判断
这里涉及到一个悬垂结构 Dangling Element的定义

一般在一个句子中，修饰语必须清楚地修饰句中某个词或短语，如果它不修饰句中的任何成分，而处于悬浮状态，这样的修饰语即为悬垂结构(Dangling Element)。

Climbing up the tower, the whole city came into our view.

悬垂结构 的理解

分词短语在句子中作状语时，其逻辑主语(亦称隐含主语)通常应是整个句子的主语；如果不是，而且其本身也不带自己的主语(如在独立主格结构中)，就被认为是一个语言失误。这个分词就叫做“悬垂分词”(dangling participle)或“无依附分词 ”(unattached participle)。例如：
(1)Getting down from the bus，my ankle was sprained．
(2)Driving to Chicago that night，a sudden thought struck me．

由 悬垂结构 造成的错误

(1)悬垂分词

误： Being Sunday, they went for a picnic.

正： It being Sunday, they went for a picnic.

正： As it was Sunday, they went for a picnic.

(2)悬垂不定式

误：To swim properly, a course of instruction was necessary.

正：To swim properly, one needs a course of instruction.

(3)悬垂简式从句

误：When a middle school student, his paren