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It is wrong the way they treat that poor an ...
Just do it the way I do.

是的。the way 的用法不一样。

第一句，the way 实际等于 how 的用法，引导主语从句（真正主语，it 是形式主语）。the way  暗含“方式”。这里 the way 就按 how 理解就行了，或者换成 that 也可。其实这三种结构，表意是一样的，相等的：

It is wrong the way they treat that poor an ...
It is wrong how they treat that poor an ...
It is wrong that they treat that poor an ...
又如：

That you can do it is possible.

How you can do it is possible.

The way you can do it is possible.

第二句，the way = as ，引导方式状语从句。也可以分解开来，去理解它的用法：

Just do it the way I do. = Just do it (in) the way (in which) I do.