Responding

One group of people get very frustrated when they send an email, make an enquiry, make a request or leave a message at how LONG it takes for the receiver to respond.

One group of people get very frustrated when they get an email, receive an enquiry, get presented with a request or get left a message at how QUICKLY the sender expects you to respond.

Which group is wrong?
Which group is right?
Why is that most people in one group are also in the other?
What can we do about it?