She was wearing the same dress that I had on（同类同物）

如果是同一时间就需要改为关系代词引导定语从句。

She was wearing the same dress as I had on.（同类异物）

解答如下：

such+名词+关系代词as/that引导定语从句可以互换情况只能是“表示抽象意义名词”时

I have the same opinion as /that you have.

理解(1)以上句子可以理解为：她穿着我之前穿过那件衣服。衣服属于“同类同物，即同一件衣服，只是2个人所穿时间不同。

理解(2)以上句子为错误使用关系代词that,应该改为as即同类不同物体。

【1】在so/such...that...引导的结果状语从句中，that不作任何成分，只起引导作用。要注意区别这两种不同的结构。

They had such a fierce dog that no one dared to go near their house. 他们家有一条凶狗，没人敢靠近他们家。  

（that引导结果状语从句，在句中不作成分）

【2】the same后有时用that，它表示“同一个，就是那一个”的意思，即同类同物；而as则表示“与……一样”，但不是同一个，即同类异物

This is the same cell phone that I lost yesterday.

这就是我昨天丢的那部手机。

This is the same cell phone as I lost yesterday.

这是与我昨天丢的相同的一部手机。

He is not such a person as you think .（定语从句）

They had such a fierce dog as I had never seen.（定语从句）

This is the same book that I lost yesterday .(同类同物)

这就是我昨天丢失的那一本书.

This is the same book as I lost yesterday (同类异物)

这与我昨天丢失的那本书一样.

I bought the same dictionary as you borrowed.（同一类的2本字典）

I met the same person that I saw yesterday.(同一个人）

We have found such materials as are used in their factory（定语从句）

These houses are sold at such a low price as people expected（定语从句）

He is not the same man as he was （定语从句）

【3】但是在抽象名词，同类事物没有绝对区别，因此as/that可以换用.

I have the same opinion as /that you have.