Do you need visas from both countries to travel to Turkey and Greece?

Yes, because Turkey is not a Schengen country. However, with a Greek visa, you can visit other Schengen countries: Austria, Belgium, Denmark, Finland, France, Germany, Iceland, Italy, Greece, Luxembourg, Netherlands, Norway, Portugal, Spain, Sweden, Hungary, Czech Republic, Slovakia, Slovenia, Poland, Estonia, Latvia, Lithuania, Malta, Switzerland and Liechtenstein.