以下是您在rextester.com/uijk63292上查询的变体

SELECT
     a_index
    ,client 
    ,variable
    ,displayname
    ,color_info
    ,clevs
    ,ccols
    ,cmin
    ,cmax
    ,cint
    ,show_on_models_quicklinks
FROM `variables_info` 
WHERE `client` = 'client1' 
OR (`client` IS NULL 
    and `displayname` IN (SELECT `displayname` FROM `variables_info` 
                          WHERE `client` IS NULL 
                          and NOT `displayname` IN (SELECT `displayname` 
                                                    FROM `variables_info` 
                                                    WHERE `client` = 'client1')
                         )
   )
;

注意：我猜您只需要client1中尚未包含的任何displayname，它由以下内容返回：

SELECT `displayname` FROM `variables_info` 
WHERE `client` IS NULL 
and NOT `displayname` IN (SELECT `displayname` 
                          FROM `variables_info` 
                          WHERE `client` = 'client1')

看到了吗http://rextester.com/llokz9426

您可以尝试使用聚合来执行以下操作，但是如果您使用的是mysql的升级版本，那么您可以使用row\ u number（）函数，这样更容易识别重复项

select variable,displayname,clevs,ccols,cmin,cmax,max(show_on_quicklinks) as show_on_quicklinks,max(client) as client
    from tablename
    gruop by variable,displayname,clevs,ccols,cmin,cmax

更改样本后修改查询：

set @client := 'client1';
set @var := (select variable from variables_info where client = @client limit 1);

SELECT
      variable,displayname,clevs,ccols,cmin,cmax,show_on_quicklinks,client
FROM (
    SELECT
          @row_num :=IF(@prev_value = concat(v.variable, coalesce(v.client,'')), @row_num + 1, 1)AS RowNumber
        , v.*
        , @prev_value := concat(v.variable, coalesce(v.client,''))
    FROM variables_info AS v
    CROSS JOIN (SELECT @row_num :=1,  @prev_value :='') vars
    ORDER BY 
        v.variable, v.client
    ) AS d
WHERE (
       (RowNumber = 1 and client = @client)
    OR (RowNumber = 1 and client IS NULL and variable <> @var)
     )

另请参见：http://rextester.com/vhndh48312
注意：上面的查询模拟了“row\u number（）”，这是一个非常有用的“窗口函数”，可以在mysql 8和许多其他sql数据库中找到。
原始：
这不是一个有效的查询，但是它从您的示例3中找到了想要的2行。

select

* 

from variables_info
where (variable in (select variable from variables_info where client = 'client1') and client is not null
     OR
       variable NOT in (select variable from variables_info where client = 'client1') and client is null
      )

请参见：http://rextester.com/taym62841
如果你有一个mysql的最新版本，那么更好的方法是可用的。