It’s surprising to see how many people confuse between the two and use these two interchangeably. This can lead to confusion and even issues while choosing the most appropriate solution for ones needs.
If you are talking about online Project Management software, then important aspects of project management have to be incorporated — like task scheduling, gantt chart reporting, resource scheduling, ability to track project timeline and milestones. Without these core features, the solution could probably be a online file share platform in a central place
If you are taking about Project Collaboration software then aspects like file sharing, file check-in/out, discussion forums, issue trackers, task assignment etc are central to the solution. Aspects like access control, email integration, mobile interfaces also become important NFR areas for such platforms
In an ideal world, (and from a project perspective, everything is one project) there should be single platform for both project management + project collaboration. There are few solutions that provide the amalgamation of the two but still one needs to be aware of which part is what.