The HAVING clause and the WHERE clause are both used to specify filtering conditions. However, the difference is that the WHERE clause filters the records before grouping, while the HAVING clause filters the results after grouping. Therefore, the HAVING clause can use aggregate functions as filtering conditions, as well as other ordinary scalar fields, and it can also be used simultaneously with the WHERE clause.

正确答案是：C: The HAVING clause is equivalent to the WHERE clause.

专业分析：

1. **A: The HAVING clause can include fields with the effect of aggregate functions as well as ordinary scalar fields.**
- 这句话是正确的。HAVING 子句可以包含聚合函数的字段，如 `SUM`, `COUNT`, `AVG` 等，也可以包含普通的标量字段。

2. **B: The WHERE clause cannot be used simultaneously with the HAVING clause.**
- 这句话是不正确的。WHERE 子句和 HAVING 子句可以同时使用。WHERE 子句用于在聚合之前过滤记录，而 HAVING 子句用于在聚合之后过滤记录。

3. **C: The HAVING clause is equivalent to the WHERE clause.**
- 这句话是不正确的。HAVING 子句和 WHERE 子句的作用不同。WHERE 子句用于在聚合操作之前过滤记录，而 HAVING 子句用于在执行聚合操作之后对结果进行过滤。

4. **D: The HAVING clause must be followed by an aggregate function.**
- 这句话是不完全正确的。虽然 HAVING 子句通常用于包含聚合函数的条件，但它并不一定总是必须包含聚合函数。HAVING 子句可以包含任何有效的布尔表达式，只不过在实际使用中，通常会用到聚合函数。

综上所述，C 选项是错误的，因为它错误地将 HAVING 子句等同于 WHERE 子句。