The reason that it's called Turkish Coffee is because the Turkish Coffee first originated in Turkey which is a country.
Turkish coffee was first introduced in Turkey in the year 1540 which was a very long time ago.
Greek Turkish Coffee is the same thing as regular Turkish Coffee.
Greek Turkish Coffee is made with a fine grind of coffee (sometimes called a Turkish grind).
The Greek Turkish coffee like regular Turkish coffee is boiled in a tall, narrow pot known as a briki, cezve, or an ibrik.
Greek Turkish coffee and regular Turkish Coffee is served with grounds in the cup and often a demitasse cup.
For True Turkish Coffee you do not strain the Turkish Coffee as it's meant to have the coffee grounds in the bottom of the Turkish Coffee.
When making Turkish Coffee you do not strain the Turkish Coffee like you would regular coffee.
Turkish Coffee is meant to have the coffee grounds at the bottom of the Turkish Coffee.
However if you prefer to strain the coffee grounds out of the cup of Turkish Coffee you can do so and still have Turkish Coffee.
To properly make Turkish Coffee you need to have the special pot (cezve or ibrik)
However you could make the Turkish Coffee without the special Turkish coffee pot but having the special coffee pot for the Turkish Coffee helps a lot in making a great cup of Turkish Coffee.
You don't have to drink the bottom of Turkish Coffee if you don't want too but I prefer to drink the bottom of the Turkish coffee myself.