Is a construction loan that is converted to a mortgage considered the same as a refinance?

No, a construction loan converted to a regular loan is generally not a refinance.  The construction loan terms are meant to be converted as part of the process.   Generally, you will have the regular loan terms in place that automatically change convert when you take out the construction loan.  

Thank you. That was what I thought, but I came across some confusing verbiage and wanted to be sure.