1) Someone else has a cell phone but has not installed the echo app.
You can now use your echo device to call them by saying their phone number or if they’re in your cell phone contact book you can use the contact name. This will also work if they have a landline.
2) someone else has a cell phone and they have installed the echo app.
If you have them in your own contact book and you have both set up the permissions in the echo app, you can also send Echo messages back and forth.
3) you have a landline, an echo Device like Dot or Echo, and and the new echo Connect box plugged into the phone jack at your house
Your echo device now becomes a speakerphone for your landline. You can call people either by saying their phone number or if they are in the contact book on your mobile phone. And now if anyone calls your landline, you can answer on your echo device.
Just think of the new echo connect device as a speakerphone Bridge between your landline and your regular echo device. But the “echo connect” by itself doesn’t do any of the regular echo stuff. It’s just going to connect your landline to your echo.
So people cannot call your echo device directly unless they have set up the echo app and you have given them permission.
The big new thing about Echo calling is that now, just with a smart phone and an echo device, you can call out and reach any number. No preapproval is required on either side. You can think of it as just turning your echo into a speaker for outgoing calls on your mobile phone number (although, as noted below, your mobile phone doesn’t have to be on and the minutes do not count against your calling plan as it’s actually an Internet call). 
And people who have land lines can now use their land lines with echo as well, both incoming and outgoing, as long as they also by the “echo connect” device. 
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Oh, and some cellular services, like AT&T, do have their own echo skills that let you send text messages from your echo using your cellular plan. But that’s a separate function.