The term packet radio is generally used to mean the same as AX.25, although other packet based protocols may also be used. Applications may use AX.25 frames directly, or they may encapsulate their traffic in TCP/IP. For quite a while now regular distributions of the open source Linux operating system have included AX.25 networking support in the kernel.
A comprehensive guide for using AX.25 with Linux is available as part of The Linux Documentation Project: Linux Amateur Radio AX.25 HOWTO V2.0 (although this does contain outdated information, last updated 2001-09-19) and a German translation of this guide (V1.6-2, last updated 1999-07-08) is available here.
The essential tools you need for configuring AX.25 on linux can be found in ax25-tools and a set of useful applications can be found in ax25-apps. If you would like to develop applications using AX.25 on Linux, libax25 provides a set of useful functions to make this easier.