I would encourage you to read the very original paper (here is a copy) ... If you read this from the very beginning, you'll find that Searle's use of three different batches of symbols is really in specific response to Roger Schank's computer program that answers questions about stories given to it.
Very briefly, and leaving out the various details, one can describe Schank's program as follows: the aim of the program is to simulate the human ability to understand stories. It is characteristic of human beings' story-understanding capacity that they can answer questions about the story even though the information that they give was never explicitly stated in the story.
Thus, for example, suppose you are given the following story:-A man went into a restaurant and ordered a hamburger. When the hamburger arrived it was burned to a crisp, and the man stormed out of the restaurant angrily, without paying for the hamburger or leaving atip." Now, if you are asked -Did the man eat the hamburger?" you will presumably answer, ' No, he did not.'
Similarly, if you are given the following story: '-A man went into a restaurant and ordered a hamburger; when the hamburger came he was very pleased with it; and as he left the restaurant he gave the waitress a large tip before paying his bill," and you are asked the question, -Did the man eat the hamburger?,-' you will presumably answer, -Yes, he ate the hamburger."
Now Schank's machines can similarly answer questions about restaurants in this fashion. To do this, they have a -representation" of the sort of information that human beings have about restaurants, which enables them to answer such questions as those above, given these sorts of stories. When the machine is given the story and then asked the question, the machine will print out answers of the sort that we would expect human beings to give if told similar stories.
The "representation of the sort of information that human beings have about restaurants" that Searle mentions in the last paragraph is what Roger Schank called a "script". Unfortunately, Searle failed at this very point in the paper to point that out ... even though in his later description of the Chinese Room scenario, he does refer to these 'scripts' ... so without that background about Schank's work, it is understandable why you would be confused!
Anyway, a "script" is a kind of representation that represents what a "typical" going-to-a-restaurant event would be like: you go in, the waiter sits you down, you look at menu, order, wait for food, eat food, get the bill, pay, and leave. So, for the second story, a basic script like that would suggest that most likely the man did eat his hamburger, even though the story never explicitly says this. And further scripts, or more refined scripts, would be able to handle the first scenario: a kind of bad-experience-at-a-restaurant script.
So, Schank's program used these three sets of symbols: the "story", the "script", and the "questions". This is what Searle replicates in his Chinese Room scenario.
That said, it is clear that Searle intends to make his argument work for any computer program. And, from that perspective, there is really no importance to the fact that there are three batches of symbols rather than, say, one, four, or sixteen. And the same goes for the English manuals that provide the rules to manipulate those symbols: there could be just one, or twenty-seven, depending on how you want to parse this up.
What is essential, is that the batches of symbols are like the representations that the computer works with, and the English manuals the programs that tells the computer how to manipulate those representations. Indeed, this is why typical expositions of the Chinese Room scenario simply talk about one rulebook for the manipulation of strings of symbols, without any further differentiation into any kinds of batches.