Is ctfr gene the same as being acystic fibrosis carrier?

Not necessarily: The CFTR gene, or mutations in this gene, are what are often being tested for in patients suspected of being cystic fibrosis carriers or suffering from the disease itself. If you are a carrier then you will have one copy of your CFTR gene with an abnormality.

They are related: Dear Jane, The CFTR gene is the gene associated with Cystic Fibrosis (CF). As we each inherit two copies of most all of our genes (one copy from each parent), we each carry two copies of the CFTR gene as well. If someone has two mutations in this gene, then they would be considered affected and will have CF. If someone only has one mutation in this gene, then they would be considered a carrier.