The two packages represent input / output formats, mapper and reducer base classes for the corresponding Hadoop mapred and mapreduce APIs.
So if your job uses the old (mapred) package APIs, then you should use the corresponding mapred avro package classes.
Avro has an example word count adaptation that uses Avro output format, which should be easy to modify for the newer mapreduce API:
Here's some gist with the modifications: https://gist.github.com/chriswhite199/6755242