就固定结构而言，你提到的六个短语这里只包括三种类型。
1、would sooner 本意是“愿意尽早”，也就是“宁可/宁愿”，和would rather或had rather表达的是同一意思（参看上次的分析）。
※ 常与 than 连用，表示“宁可…也不”，例如：
* The soldier would sooner die than surrender. 这个战士宁死不降。
* They would sooner starve to death than eat food handed out in contempt. 他们宁愿饿死也不食嗟来之食。
* I would sooner go to bed earlier than do such a thing. 我宁可早早睡觉也不愿干这样的事。
※ 有时在语境明确的前提下， than从句常省去，上面的例句就可以改写为如下：
* The soldier would sooner die. 这个战士宁可死去。
* They would sooner starve to death. 他们宁愿饿死。
* I would sooner go to bed earlier. 我宁可睡觉。
2、sooner … than
1） 在否定结构no sooner 中，than引导
比较状语从句，表示“刚一…就/没等…就”。
※“no sooner +
过去式 + than”表示
主从句中动作在同时发生。如：
* No sooner learned than (it is) forgotten 边学边忘.
* No sooner said than done, procrastination is the most time. 说干就干，拖延就是浪费时间。
* When he said he wanted to go to the zoo on his birthday it was no sooner said than (it was) done. 他一说他生日那天想去动物园，立刻就照做了。
※“no sooner + 过去完成式 + than”表示主从句中动作几乎就在同时发生。如：
* He had no sooner come than she left 他刚一到，她就离开了。
* I had no sooner left than she called 我刚走她就打来了电话
* He had no sooner returned than he bought a house and went to live there. 他刚一回来便买下了一幢房子住了进去。
※ 以上句式还可以用倒装结构，如：
* No sooner had we
set out than a thunderstorm broke. 我们刚出发就碰上了一阵雷雨。
* No sooner had I lain down than the telephone rang. 我刚躺下, 电话铃就响了。
* No sooner had he arrived than the trouble started. 他刚一到，麻烦就来了。
* No sooner was it said than (it was) done. 刚一提到立刻就照做了。
2）直接使用sooner than，表示“比…更早/比…更快”，如：
* Nothing dries sooner than a tear. 眼泪干得最快。
* Ill air slays sooner than the sword. 污浊的空气杀人比刀还快。
* Some people become prosperous sooner than others. 一部分人先富裕起来。
* She will be here sooner than you expect. 她很快就到，比你预料的要早。
3、
as soon as与no sooner … than同义，二者可以互换，但主从句位置不同。
* He had no sooner come than she left 他刚一到，她就离开了。
改写：
——He came as soon as she had left. 她刚离开他就到了。
——He came as soon as she left. 她一离开他就到了。
* I had no sooner left than she called 我刚走她就打来了电话
改写：
——I left as soon as she had called. 他刚打过电话我就走了。
——I left as soon as she called. 他一打电话我就走了。
* I had no sooner returned than he bought a house. 他刚一回来便买下了一幢房子。
改写：
——He returned as soon as I had bought a house. 我刚买下房子他就回来了。
——He returned as soon as I bought a house. 我一买下房子他就回来了。
追问下面是老师您写的两句话。
请问：为什么第一句的as soon as后面是过去完成时，第二句的as soon as后面是一般过去时？有什么区别吗？
1.He came as soon as she had left. 她刚离开他就到了。
2.He came as soon as she left. 她一离开他就到了。
追答1. He came as soon as she had left. 她刚离开他就到了。—— “离开”和“到”两个行为有时间差，即先离开后到。
2.He came as soon as she left. 她一离开他就到了。——“离开”和“到”两个行为几乎没有时间差，即在离开的一瞬间他就到了。