They have their best clothes on.

on是副词，作宾语补足语。have sth on.穿着，戴着衣服、帽子等。

She bought a bookself to put her books on.

on是介词，不定式短语to put her books on作bookshelf的定语，被修饰名词是不定式短语中的介词的逻辑宾语。=a bookshelf on which to put her books. = a bookshelf on which she was to put her books.

qif2007老师介绍的后现代语法将方位副词归为介词，而介词的定义不同于传统语法和夸克语法中的介词的定义。因此在你没有了解后现代语法的前提下，不宜持此观点。还是将应将方位副词和介词视为两个不同的词类。