PASMO is a prepaid IC card issued by the Tokyo Metro which can be used to travel on the Metro, JR and other trains. Just touch the card on the card reader when you start and end your journey.
Both cards can be purchased at stations in Tokyo. In other major cities (Osaka, Fukuoka, Nagoya Sapporo) also offer similar IC cards such as ICOCA, Kitaka, Sugoka, Manaca, Nimoca etc. which can be used throughout Japan.
ICOCA is a prepared IC card issued by JR West rail network in the Kansai (incl. Osaka and Kyoto). It is a convenient, all-in-one travel card for JR West trains, subway, private railway, and buses, and other major cities (Tokyo, Fukuoka, Nagoya, Sapporo). And also participating shops in the station and around town displaying the ICOCA marks. Before you leave Japan, this ICOCA refund can only be done at JR West Area (Kyoto/Osaka/Kansai area).
Suica is a pre-paid IC card issued by JR East to travel around Tokyo and also other major cities in Japan. It also can be used for shopping at registered shops including major convenience stores, shopping malls AEON, electronic stores BIC Camera and Yodobashi Cameras and many more.