【请问ON THE WAY和UNDER WAY什么区别？】

on the/one's/its way
a) arriving or happening soon(即将到达或发生):
There's a letter on its way to you.(有封给你的信就要到了。)
More changes are on the way.(更多的变化就要发生。)
b) travelling towards a particular place(向特定的地方走去):
She should be on the way here by now.(到如今她应该来这儿的路上了。)
The ships were already on their way to the gulf.(船队已启航去海湾的途中了。)
c) while going from one place to another(从一个地方去另一个地方途中)
on the/one's/its way to/out/home etc
I ran out of gas on my way to the airport.(我在去机场的途中跑得上气不接下气了。)
Guess who I bumped into on the way home.(猜猜我回家路上碰到谁了。)

be under way
a) to have started to happen or be done(已经开始发生或被作):
Plans are well under way for a new shopping centre.(新的商业中心正在很好的筹划中。)
The tournament got under way on Friday.(联赛于星期五已着手进行了。)
b) to have started to move or travel somewhere:(已经开始向某地启程了)
Our train was already under way.(我们的火车已经启程了。)

on the way 意思是“在路上、在途中”

而 under way 指的是计划，行动“正在进行中”

on the way 是指“在途中，在去……的路上(on the way to ……）”
under way 是指“在进行中”