because可以和后面的分句独立成句，它是一个承前省略句，because引导的是原因状语从句。而That is because...中because引导的是表语从句，两句话中从汉语意思来说一样，但从句子结构来说不一样，希望我的回答对你有帮助。

作为连词的 because 不能和后面的分句独立成句吧？

但是为什么会有 That is because...

连词（conj.）中，是不是只有 because 能这样用？

回答如下：

你所提的问题可以归纳为以下几点：

(1)because 当作连词，可以独立成为一个分句用来回答疑问词why引导的特殊疑问句。

-Why didn't you go to school yesterday?

你为什么昨天没有上学？

-Because I was ill.

因为病了.

(2)because 当作从属连词

A:可以引导原因状语从句，用来说明主句动作发生的原因.

I study because I want to learn.  

我学习是因为我想学到知识。

I bought the house simply because it was large.
我购买了这房子，只是因为它面积大。

An argument was inevitable because they disliked each other so much.
争论是不可避免的，因为他们彼此非常厌恶。

Just because they make more money than I do, they think they are so superior.  

只因为他们挣钱比我多,他们就认为自己高人一等。

Because I was ill,I didn't go to school yesterday.   
因为病了,所以昨天我没有去上学。

You shouldn't get angry just because some people speak ill of you.   
你不要因为有人说你坏话而生气。

B:可以放在系动词后,引导表语从句.(It/That is/was because...结构）

If you feel cold, it is because you didn't put on your overcoat.  

如果你感到冷的话,那是因为你没有穿上外套。

This is because the earth is travelling round the sun.  

这是因为地球在围绕太阳运转。

This is because the direct current flows in a wire always in one direction.  

这是由于直流电在导线内总是沿着一个方向流动。

C:用在强调句结构中

It is because he is honest that we like him.   

是因为他诚实我们才喜欢他。

D:还可以用在否定转移句子中

I didn't go because I was afraid.   
我没有去是因为怕。/我不是因为怕才去。

I didn't go, because I was afraid.   
我没有去是因为怕。