You can also make data calls over GSM without the need for GPRS:

GSM Originally stood for "Group Special Mobile" - being the name of the ETSI committee that defined the specs.
Once the specs were done, it seemed silly to be still calling them after a committee, so they re-branded it as "Global System for Mobile communication" - which is pretty accurate and descriptive.
You can download all the specs for free from: http://www.3gpp.org/

GSM is the Digital Cellular ("mobile phone") standard used in Europe and many other parts of the world.
In addition to voice calls, GSM supports many other services including Circuit-Switched Data, Fax, SMS (Text Messaging), etc.

Many manufacturers produce GSM "modems" which can be used in very much the same way as a normal land-line modem - with an RS232 interface, AT Commands, etc, etc.
Top names include Siemens, Sony-Ericsson, Wavecom, Falcom, Multitech, et al
You can also buy "modules" that contain just the "guts" of the modem on a "naked" board for embedding into other products - these would usually lack such things as enclosures, power supplies, RS232 transceivers, SIM holders, standard connectors, etc, etc. They may also require additional type-approval work.

GPRS is the General Packet Radio Service - it builds on the underlying GSM infrastructure to provide IP-based (packet) data services.
Use of GPRS requires an IP protocol stack.
Again, many manufacturers produce GPRS "modems" - some of which have TCP/IP built-in.
(in fact, you'd find it hard to find a current GSM "modem" today that didn't support GPRS!)

CDMA is Code-Division Multiple Access, which is a technique used in a number of communications applications. In this context, you are presumably thinking of the system championed by Qualcomm as an alternative to GSM.

DTMF is Dual-Tone, Multi-Frequency and has nothing specifically to do with wireless communications at all!
It was developed as a technique for in-band signalling (look it up) in wired telephone systems - also known as "Touch-Tone"
You should not attempt to send DTMF through a GSM phone link! (the GSM audio processing messes it up).


Buy a modem.
Get it working with a modem, then move on to a module if required.

Use the Search facility on this site, as it has all been discussed plenty before already...