The boy ran towards her as soon as he saw her mother approaching.

The boy ran towards her when he saw her mother approaching.

这两句话的连词是不是都可以，意思上有区别吗？

这两句话都对。如果说区别，多少还是有的，就是在时间的衔接度上略有区别，看翻译：

1. as soon as：一（从句）......就（主句）

2， when：在......时（从句），......（主句）

此外，建议把名词词组 her mother 放在主句中，把代词 her 放在时间从句中。就是说，把名词和代词调换过来。

The boy ran towards her mother as soon as he saw her approaching.

The boy ran towards her mother when he saw her approaching.