Alerts indicate WHERE the service should track for new comments - basically it's a link to a social community, an advertising post or just a key phrase that you define.
Projects are used to organise and manage Alerts and their behaviours. They decide WHAT TO DO with comment alerts. They determine where to send alert notifications, the frequency of alerts delivery, and control what is filtered into or out of the alerts themselves.
Please watch the full explanation in the video:
Also please note, that every account in Chotam has at least one default Project to which all created alerts are assigned by default, but you can change that. You can create as many Projects as you like.