Yes, in this world, anyway. There is a canon difference between mediwizards and Healers, or there wouldn't be a reason not to call Madam Pomfrey a Healer. I think it's more likely the mediwizards have less training and aren't as trusted.

As will be revealed in the future, Harry actually did sit his NEWTs again, and failed the Potions practical again. I am evil.

And thank you!