What are the differences between a Unified Group and a SharePoint site?

Unified Groups are exactly what they sound like, groups that incorporate features from various O365 products in one unified feature.  These groups have simplified and stripped down functionalities designed to make self management more simple, at the cost of customizability. They include a group Distribution List, Calendar, SharePoint Site and can be self managed and created.

A full fledged SharePoint site doesn't have an email address or a calendar like a Unified Group does, and includes the full featureset for SharePoint.  Site collections must be created by HUIT, or sites can be requested through Self Service Site Creation.
See also: SharePoint