The ax25-apps package contains programs for the hamradio protocol AX.25 that would be used by normal users (as opposed to network daemons). While not essential, these programs are usually installed if you want to connect to amatuer packet radio networks. Generally it is a good idea to also get the ax25-tools package so you can configure the hamradio ports. This package includes call, listen, ax25ipd and ax25rtd.
The ax25-tools package contains the tools that you need to get going with AX.25 for Linux. AX.25 is a network protocol that is used by hamradio operators across packet radio wireless links. This package contains the network tools to configure hamradio interfaces and some of the hamradio specific network daemons. In addition to programs that understand AX.25, they also work with ROSE and Net/ROM hamradio protocols.