Customers can now sit down comfortably while they 'wait' for their number to be called out.
You are asking about the difference between they wait and they are waiting in this sentence.
First, let's see what the progressive or continuous aspect brings to the table. It is called continuous because it presents the activity of the verb as having duration. Thus the action of the verb waiting can be depicted as a wave ~~~~~~~~~~.
The action of a non-progressive verb, such as wait, can be depicted as a discrete event which has a distinct beginning and ending. This is easier seen in verbs like jump, but the same goes for wait. The action of a non-progressive verb can be depicted as an X.
2 I jump onto the chair.
jump is an action that has a discrete start and finish, and the event jump is seen as a whole, as a point in time, thus as an X.
3 I am jumping onto the chair.
jumping is seen as having a duration. Therefore, the action of jump is s-t-r-e-t-c-h-e-d o-u-t before you. It doesn't slow time down, but what it does is expand the punctiliar event into an event or action having duration. So you are depicting jump as a ~~~~~~~~~~~~~~~ in your brain.
Note that the difference between seeing jump or wait as a single event X and as an event having duration is psychological. The real time that it takes to jump onto the chair is the same whether in the simple present or progressive present.
Let's get back to wait(ing) for their number to be called out.
4 They wait for their number to be called out.
is looking at the event wait in its entirety, but as taking a point in time. While
5 They are waiting for their number to be called out.
in your mind, you are depicting the action of wait as having duration, so that it stretches out ~~~~~~~~.
But there are a couple more differences. An important one is that although the progressive or continuous has a duration, it has a limited duration. It does not go on forever, it will end at some point in the (near) future.
You may be depicting jumping as a duration, but as soon as you reach the chair, your jumping is over. As for they are waiting: at some point, their number will be called and the waiting will be over. That is, the ~~~~~~~~ does not go on into infinity, rather it just goes into the near future. (Of course, when you are waiting for something, that near future can seem like an eternity if you are impatient.)
Perhaps a better example that shows the limited duration of the progressive aspect is to compare:
I live in China.
I am living in China.
The first, in the so-called simple present, depicts an "event" that actually refers to past, present, and future time. The person who says that sentence has lived in China for some indefinite past time, at the present, and infers that he or she will continue to live in China for some indefinite time into the future. There is no sense of the event ending.
But the person who says the second sentence is depicting an event "living" which is subject to change, temporary, and that will have an end. It is as if he or she says *I am living in China now, but I don't know how long this will be true."
ACTION IN PROGRESS
Another thing that the continuous or progressive aspect brings is the notion of an action in progress. Thus both I am jumping onto the table and They are waiting can refer to a duration ~~~~~~~ that is in progress as seen from some moment. This moment can be the moment you are observing this continuous action or the moment of speaking.
This is why the phrase while you wait is popular. Think about it. You bring your shoes into to be fixed. You see a sign that says
Shoes mended while you are waiting.
Golly, this presents the action as having duration ~~~~~~~~ that extends to some point in the "near" future. Already you are tired of waiting. You do not want your action of wait to be a ~~~~~~~~~. And you do not want to depict the action of fixing your shoes as in progress. You would rather see it as a punctiliar event. And stores know it too. And store owners; thus the stock phrase While you wait does not determine the meaning of this sentence, but the meaning of while you wait gives rise to the stock phrase. You think of the activity of wait as a point in time, as an X rather than as a duration ~~~~~~~~~.
To sum up,
Customers can now sit down comfortably while they wait for their number to be called out.
Both verbs are in the simple present. In this sentence, the most probable interpretation is that it refers to a situation that is 'always true'. It is similar to I live in China. The whole sentence containing sit down and wait refers to a situation that is always true. The actions sit down and wait are seen as having no definite beginning in the past, include the present time, and extend indefinitely into the future. This is similar to 'Two plus two equals four'. This use of the present does not take place at the time the sentence is said. It is true at the time it is said but it does not take place at the time it is said. (The only way this sentence can take place at the time it is being said is during a demonstration, that is, when the speaker is demonstrating something But that is not the case here, in the most probable meaning of the sentence.)
Customers can now sit down comfortably while they are waiting for their number to be called out.
The tense of the independent clause ('Customers can now sit down comfortably') is the same, therefore the overall meaning of the sentence as expressing something that is always true is retained. But now, when you use the progressive or continuous with the second verb waiting, you are depicting wait as a duration ~~~~~~~~~~~~, so the action is stretched out into a duration, rather than depicted as a point X.