Traditional Marketing

This is the marketing advertising mix that's prevailed over the years and has been perfected through broadcast and mass media techniques supported by a ratings system. It also could include some traditional PR, direct etc.

Tradigtial Marketing

Digital marketing has moved beyond it's infancy years and matured into something that's partially interactive, holds more promise for engagement, but incorporates traditional methodology. For example, a traditional Website may be interactive and technology dependent, but doesn't allow for user participation, feedback mechanisms reviews etc. Engagement can be increased through tactics such as interactive games or even a rich user experience, but there are no social components. Search methodologies are limited to things such as keyword, search optimization etc. 

Social engagement

Social engagement is created when design for participation is the primary strategy for the associated initiatives. Tactics can range from the simple to complex, but is primarily tasked with facilitating interactions from participant to participant to organization to participant(s) and vice versa. Social engagement carries distinct characteristics compared to "tradigital" in that it requires not only technology, but human intervention on the part of the organization in order to achieve the highest levels of engagement.

via David Armano