In ant a project is what you define in your build.xml file.
This project is a collection of targets, which are composed
of tasks.
In Maven a project is what you define in your project.xml file. It's a collection of information about the development effort that Maven uses to produce an artifact such as a jar or war.
A target is the unit of execution for a user of ant. When you execute ant, you provide a list of targets to run, e.g.
ant clean compile
Which executes the clean target followed by the compile
targets you have coded in your build.xml file.
In Maven, the goal is the equivalent of an ant target, e.g.
maven clean java:compile
Executes the clean goal of the clean plugin,
followed by the java:compile of the java
plugin.
Maven goals can contain ant tasks as well as jelly tags.