Original Message

Commuting is you driving yourself from where you live to your workplace.

Deadheading is you travelling for the company to a place where they need you, from your home or domicile.

A relief pilot/pool pilot is not driving himself to work, he is travelling for the company.  He is home based.  They need him/her somewhere and assign it to him/her and provide the travel, be it POV/commercial transportation.  That pilot is working for the company for that transportation and thus on duty.  That duty counts towards his rest limitations.

A commuter's time spent to/from work is of the pilot's own doing.  That is not duty!

So, a relief pilot travelling to a base starts his duty time when he leaves the home to travel to the work assignment.  That's duty time.   That duty time ends when s/he is back home, or in a hotel/adequate rest facility.   

A pilot needs to have 10 hrs of rest in the last 24 hours looking back from when a planned PART 135 flight lands.   The deadhead time in front of the day's "shift" is part of that lookback!