This also puzzled me a bit, and although this is an old question, I thought I would expand on @Jan's comment with some content from the discussion related to it, as this might help other users.
From the Jenkins CI forum :
A project is a special case of work, i.e. all projects are tasks, but not all jobs are projects.
Perhaps this helps to mentally extend the names to “common goals,” jobs and “software projects” (although the latter are not needed to create software, they are adapted to this use case).
In the case of a “new job,” Jenkins still does not know whether the new job will have a subtype of the project. On the other hand, once you have chosen to create a project, this is reflected as specific as possible in the user interface ("Project Foo"). If you look at the exact wording in the “New Task” page, you will understand the subtle differences (for example, “Create a free style software project” as opposed to “Monitoring an external task”).
An example of a task that is not a project is the lesser known “external work”, which receives notifications of events that occur outside of Jenkins, but should be monitored inside Jenkins (for example, reboot systems, etc.). See https://wiki.jenkins-ci.org/display/JENKINS/Monitoring+external+jobs for more about this type of work.
For records, this is the actual class model used by Jenkins domestically (extension of subclasses indented below their superclass):
Job AbstractProject MatrixProject (aka "multi-configuration project") Project FreeStyleProject MatrixConfiguration (a single configuration of a matrix project) StubJob ViewJob ExternalJob
Only FreeStyleProject, MatrixProject, and ExternalJob are visible on the New Job Page.