You buy the phone and it comes with so many minutes. You activate it and you have a phone number. You can add minutes as you wish. Every time you add minutes, you get a new expire date, like if you don't add then the phone will go dead on a certain date.
I think the Anthony's bought these when Casey got out on bond thinking they would circumvent any taps on their known phones and could keep these secret from LE. (And I think via DC LE now knows these phone numbers and is learning all sorts of interesting things. And they will share it with us sooner or later.)
I think the company does have records just like a regular phone, although unless one registers the phone , they don't know who you are. I forget, you can add time two ways, one go back to the store that sells the phone and get a time card for your phone, or the other way is to use the phone to add time via a credit card.
I have used a Verizon PrePaid for almost two years (same number). The reason is DH and I had cells with ATT, then, when our contract was close to up, he got a new one through his employer. There was no point in his having two, as he has unlimited 24/7 usage. I hardly used mine, I am at home all day and just didn't see paying for the new contract for how little useage there would be. So I bought a prepaid Verizon as Dh's company phone is Verizon. It costs me 15 a month, which seems better than the ATT. Mine is registered as I normally reload mine via CC. If I don't use all my time, it rolls over, but,I still have to add the 15.00 monthly to keep it going. If we are going out of town I can add more at will, as my phone will go online (for .99 per day) and I can browse or check email.
I think their are good reasons for these kinds of phone as well as the evading LE.