Microsoft project management software used to plan, manage, and communicate a project schedule and other information among workgroup members, project managers, and other stakeholders.
And.Jann1,
I know very little about Project for the Web except that it is very limited, I use the standalone desktop version of Project. If you access Project via a URL that contains "project.microsoft.com", then what you have is indeed Project for the Web.
Regardless of the version, as I noted previously, no version of Project will automatically distribute resources to tasks based on resource capacity or availability.
John