This article is from the Anime FAQ, by Steve Pearl with numerous contributions by others.
These are actually two different things.
Ma Bell in Japan is still a national monopoly / government bureacracy. Nippon Telephone and Telegraph (NTT) charges 10 yen per time unit for local calls. 10 yen coins are an annoyance to carry around. Sort of like a pocket full of nickles. But if you stuff a larger denomination coin into a phone, you don't get change for time/money not used. Enter the telephone card. It is a cheap piece of plastic the size of a credit card with a magnetic widget inside. You buy them from a vending machine or a kiosk (in denominations ranging from 500 to 5000 yen). The green phones are (mostly) wired to accept phone cards (yes, there are different color phones depending on the type of call). Stuff a telephone card into the slot and you don't have to worry about carrying around a pocket full of nickles and the magnetic widget counts off each time unit as you use it. There cards are particularly useful for international calls. Each time unit costs 100 yen and they count off very quickly.
With all these little plastic cards running around, somebody in Japan got the idea of putting pretty pictures on them. Like mountains, or rivers, or forests, or movie stars, or whatever. Certain types of fans like to collect these cards (sort of like a cross between expensive postage stamps and baseball cards). For these fans, companies print up limited runs of cards with desireable pictures on them and then sell them for double the face value (spend 1000 yen to get a 500 yen card). The fans value these cards as long as they are not used at all. So they are another anime/manga collectable.
- from a post by Eric Kouba - Phone Books
This is a term used to describe the various manga magazines. These periodicals are typically printed on newsprint, and contain several ongoing manga stories (which, if popular, are usually collected into collections). These magazines are VERY thick and often resemble phonebooks.