Yes. As a certified reiki master teacher (Usui reiki) I can say we are certified first in reiki 1 which gives us the ability to heal ourselves – mind, body, spirit.
Then if we wish, we can get certified in reiki level 2 which gives us the ability to heal ourselves and others on a mind, body, spirit and emotional level. At this level we can work as practitioners in reiki (energy healing) on our own or at places like spas. We also qualify for reiki insurance if we wish to work on others. Reiki level 2 also attunes you to the distance symbol so you can send reiki and provide reiki to anyone or anything (plants, animals, etc.) around the world.
Then if you wish to pursue further reiki training you can. Some get attuned to reiki master symbols without training in teaching while others also get trained to teach and attune others.
The answer to your question is yes. A reiki master or reiki master teacher is also a healer. With each level of attunement and certification we get attuned to more symbols and open our energy up more and the like.