Semantics and Grind sizes
Turkish coffee and French press can either refer to the method of brewing coffee, or on some ground coffee packaging, can refer to the grind size; Turkish coffee traditionally uses a fine grind, whereas french press traditionally uses a much coarser grind.
Arabica and Robusta are species of coffee, where arabica is universally considered to be the better tasting. The beans you buy may be single origin coffees, which means that all the beans come from a single coffee plantation, or they may be blends of different single origin beans, even blends of arabica and robusta coffees together.
Traditionally turkish coffee involves mixing fine ground coffee with water and bringing it to the boil on a stovetop. Once the coffee reaches the boil and it has cooled enough to drink it is ready. Usually this is done using a cezve or ibrik (https://en.wikipedia.org/wiki/Cezve)
French press (plunger coffee) involves adding boiling water to coarse ground coffee and steeping the coffee for about 3-5 minutes before plunging the filter to filter out the coffee grounds. To brew French press requires a... french press
If you'd like to learn more about different coffee preperation types, wikipedia has some really good information: https://en.wikipedia.org/wiki/Coffee_preparation
Source: I'm a barista.