Difference between "the" and "that"

I wonder what the difference between the and that in this context is:

A: Hey, I've heard we have a new printer.
B: Really? Let's print the documents on the/that new printer then.

I think the two real choices are:

• Let's print the documents on the new printer then.
• Let's print the documents on that printer then.

Both the above seem pretty much identical in meaning to me. The second can only be used following a mention of a specific printer, or accompanied by physically indicating a printer. The first can be used in those contexts but doesn't require any context of that sort.

Only if there were several new printers and someone had previously referred specifically to one of them (e.g. "One of the new printers is fast!") would I write or say:

• Let's print the documents on that new printer then.

Short Version: Articles (the) help specify certain characteristics of nouns (definiteness, number) Whereas demonstratives are mainly reserved for selection (that one) and spatial deixis:

(bring that, and let me hold on to this)

In this particular case, the meaning of the sentence changes very little. However, in English, there are subtleties in the function of seemingly interchangeable words.

The is a definite article. It functions only as an adjective and has no tense. In this case, it's used to identify a primary printer. Most people hear the and tend to lean towards "singular, the main one" even if the following noun is plural. In this example, the is used to round multiple nouns into a single unit:

We need to remember to feed the dogs before we leave. (The turns multiple dogs into one group of dogs that needs feeding)

The performs a function that can only be accomplished by an alternative demonstrative:

We need to remember to feed those dogs before we leave.

Demonstratives such as this, that, those, and these COULD perform the same job as an article, but due to all the variations, they are more flexible than simple articles:

Those (sandwiches) were delicious.

In that sentence, those performs the same job that the might do. but if you take out the word sandwiches, it becomes a pronoun with sandwiches as its antecedent.

These various words all seem more or less interchangeable, but one of the most important functions of demonstratives is something called spatial deixis, where the message can change based on the speaker/reader's physical surroundings. Similar to words like there and here, they are a little more descriptive (therefore more effective) than articles. This difference is practically negligible until multiples are involved and such details are needed to preserve the clarity of the sentence:

I want those printers to get here so we can throw these printers out.

We have to use this printer because that printer is broken.

In these examples, if we had used definite articles, they would have looked like this:

I want the printers to get here so we can throw the printers out.

We have to use the printer because the printer is broken

The sentences are now unclear because we lack certain details that definite articles can't deliver. Keep that in mind when choosing a word.

Sorry for the lengthy response. Demonstratives are really tricky since they often have little effect on the meaning of the sentence. The only thing changing is specificity and details.