1. wait (for sth/sb)（尤指长期地）希望，盼望，期待 to hope or watch for sth to happen, especially for a long time
比较偏重于“等待”这个动作持续了很久，并且这个等待的过程中很少从事其他活动的意思，有时暗示某人（事物）来得太晚或某事发生得太迟或时间流逝且含有耽误之意等：
Why are you shanding here?I’m waiting for John?
你站在干嘛呢？我正在等John。
Leeds United had waited for success for eighteen years.
利兹联队企盼夺冠已经十八年了。
This is just the opportunity I've been waiting for.
这正是我一直在期待的机会。
He's waiting for me to make a mistake.
他正盼着我出错呢。
[VN] I waited my chance and slipped out when no one was looking.
我等待时机，趁没人注意时溜了出去。
When we came home we had a meal waiting for us
我们到家时，有一顿美餐正等着我们享用。
《柯林斯高阶英汉双解学习词典》
He waited patiently for her.
他耐心地等待着他。
I've been waiting here for 2 hours!! Why are you so late, Thomas.
我已经在这里等了两个钟头，Thomas你怎么那么晚吶？
She awaits his answer.她等候他的答复。
试比较：
I’m waiting for guests.我在等客人。（表示等了很久，而且是专门等着）
I’m expecting guests. 我在等客人。(侧重于我心理在期盼着客人到来，不排除在等的时候从事着其他活动的可能性。)
2. expect sth/sb希望，盼望，期待；（常用于进行时）
to be waiting for sb/sth to arrive, as this has been arranged
侧重于某人心理状态在期盼着等待着，不排除在等的时候从事着其他活动的可能性。指对未来发生的事情有较大的把握，含有期待之意，也指预计某事或某行动的发生。
expect a visit/call/letter from sb
等待某人的来访 / 电话 / 来信
Are you expecting visitors?
你在等客人吗？
I am expecting several important letters but nothing has arrived...
我正在等几封重要的信件，可是一封都没到。
I’m expecting a telegram.我在等（盼）着一份电报。
I’m expecting John any minute now.我盼望着John很快回来。
I was expecting him yesterday.
我昨天一直在等他。
We were expecting him to arrive yesterday.
我们一直盼望着他昨天到达。
Hi, are you expecting a parcel here?
喂，你是不是在这儿等包裹？
To be frank, we are expecting visitors this evening.
说实话，我们今晚有客人。
My supervisor was expecting a phone call from me last Friday, but I totally forgot to callback. 我主管上礼拜五在等我的电话，但我竟然完全忘了要回拨。
最后分享几个正误用法：
他在校门口等他母亲。
误：He was expecting his mother at the school gate.
正：He was waiting for his mother at the school gate.
我们在等乔治的来信。
误：We are waiting for a letter from George.
正：We are expecting [looking forward to] a letter from Goerge.
那么我 10 点整等你。
误：Then I’ll wait for you at exactly ten o’clock.
正：Then I’ll expect you at exactly ten o’clock.
