转换一下句型你就清楚二者的区别了：

The president was reported to have been flying across the Atlantic.

= It was reported that the president had been flying across the Atlantic.

即总统的班机在从之前的某个时候到媒体报道的时候这段时间一直在大西洋上空飞着。动作从过去持续到报道的时候，可能刚结束，也可能没有结束。

The president was reported to be flying across the Atlantic.

= It was reported that the president was flying across the Atlantic.

即总统的班机在媒体报道的时候正在飞越大西洋，飞机的飞行正在进行，肯定没有结束。