GSM
Global System for Mobile Communication.
GSM is the dominant 2G digital mobile phone standard for most of the world. It determines the way in which mobile phones communicate with the land-based network of towers.
GSM is one of two major mobile phone technologies in the U.S. The other is CDMA. AT&T and T-Mobile use GSM. Sprint and Verizon use CDMA. GSM is more prevalent in most other parts of the world, and especially in Europe.
Although GSM and CDMA provide similar basic features and services to end-users, (such as voice calling, text messaging, and data services,) they operate very differently at many technical levels. This makes GSM phones completely incompatible with CDMA networks, and vice-versa.
The most visible feature of GSM are SIM cards. SIM cards are removable, thumbnail-sized smart cards which identify the user on the network, and can also store information such as phone book entries. SIM cards allows users to switch phones by simply moving their SIM card from one phone to the other.
GPRS
General Packet Radio Service.
A packet-switched technology that enables data communications.
GPRS is used for various data applications on phones, including wireless Internet (WAP), MMS, and software that connects to the Internet. Basically, any network connection that is not voice or text messaging uses a data connection like GPRS.
GPRS offers a tenfold increase in data speed over previous (circuit-switched) technologies, up to 115kbit/s (in theory). Typical real-world speeds are around 30-40 Kbps.
Newer technologies like EDGE and 3G are much faster.
See: EDGE
Using a packet switching, subscribers are always connected and always on-line, so services will be easy and quick to access.
GPRS is considered a "2.5G" technology, meaning it is more advanced than standard 2G digital technology, but does not meet the requirements of a full-feldged 3G technology.