As far as l know, and based on the searches I made about these two terms, an Aesthetician and an esthetician are both the same in that they are licensed specialists that provide beauty treatment to people. However, one major difference that can be noticed is where both work or where they are employed.
The term aesthetician is used for those who are employed to work in a medical facility such as clinics, hospitals, health centers. In contrast, estheticians are experts you would meet in salons, spa, and other places where beauty treatments are given. Aestheticians and estheticians help people to analyze their skin and help them to think of different methods that suit their skin for cleansing.
An aesthetician is also known as a paramedical aesthetician or a clinical aesthetician. The work of an aesthetician is basically to provide beauty treatment for patients with burns, damaged skin due to surgery, chemotherapy, etc.