I used both.I only cancelled my visa when I moved to another school after 3 years.It was then that I went to Laos to get a tourist visa.Then I looked for a new school.I just surrendered my WP to my liaisson officer and he cancelled it for me.
The liaisson officer from the new company did all for me.I only called my former boss and she communicated with my new employer.I resigned end of October 2009 but I was able to use my visa until end of March 2010 without leaving the country.
In my experience when I was in Thailand, yes.They called it Transfer of Visa.Your liaisson officer must contact your old employer to send a letter to your new employer that they're allowing you to use your old visa and be transferred under the name of your new school/company.