Internet Air

This should be posted in the internet section so we'll just move it on over to there.

But as the second part of your question, Air printers require you be connected to the same Wi-Fi

Thanks ,To clarify, I mean the new Internet Air service where the customer receives an Internet Air Hub

And the question of how two devices of the same user in this case a laptop can send a document to be printed on a printer that does not have a router at home

 make sure I understand it simply, the Internet Air Hub functions like a router for communication between the devices at home such as printing, file sharing, media streaming, etc.

Yes.  It's a stationary hotspot.  It acts as a modem and router all in one device.

What did you think it was?

I thought it was some kind of wi fi extender, thanks for the help

It wouldn't matter if it were a Wi-Fi extender. You still have to have both the source device, laptop, and a air printer connected to the same Wi-Fi .  Which means they would have to probably be in the same dwelling.

Give them a break.  Most people don't know that WIFI isn't the Internet.  Here's how it works, AT&T's internet air, received its internet signal using 5G cellular signals. Just like your cell phone does.  Now in order to get that signal to the devices you have at home, like a laptop, iPad, desktop computer, Roku, Google Chromecast, Apple TV, printer, etc, you need a WIFI router. The Wi-Fi router connects those devices to the 5G signal. It makes sense that the device AT&T would send you, would be capable of communicating with all of your devices.  I would even bet it hasn't ethernet cable in the back of it so you could probably use your existing router.  Remember there is a difference between a router and a modem.  If you want further explanation try googling. 

So it's like a normal internet service that provides a modem with 5G connectivity which I connect to the router at home to which the other devices are connected

@mathewspacc 

Oh I'm well aware they don't get it. We flag posts every day in the wireless forum because people don't understand the difference between wireless and Wi-Fi so they post internet questions and problems in the wireless section of the forum.  

And probably once a month I explain the difference between internet and Wi-Fi and wireless, so that people will use the correct technology when speaking to their service provider. 

    When you use the wrong terminology, it's like asking your auto repair person to refill your blinker fluid. They then know you have absolutely no clue what you're talking about.  😑

That's when you get taken advantage of, sold something you don't need, lied to, etc.