People often use these three terms interchangeably, but there are differences.
A visa is a conditional authorization granted to a foreign student to legally enter, remain, and leave and come back to France. A visa is the stickerlike document placed in your passport that indicates your status. Most students are given a VLS-TS étudiant visa. A VLS-TS visa is one that is valid for more than four months. If you are not an EU citizen, meaning you do not have either a passport nor a national identity card from a member state of the EU, you need a French student visa to both legally stay and study in France for more than three months.
A carte de séjour is a type of residence permit, or temporary identity card. It is the size of a debit or credit card. A carte de séjour also indicates the status you hold. For example, you will hold the status of student because you are in France for more than three months in order to study. Other students and people you meet may have a carte with a different status, such as spouse, working, or refugee. Please be aware that you cannot pick up your first carte de séjour until after you renew your student visa for the first time, which takes several months.
Students from an EU member country who hold a residence permit, rather than a passport or national identity card, may still need to obtain a student visa, depending on the type of residence permit they were granted. Please make sure to speak with Academic Programs International (API), which helps students obtain a student visa from their home country or country of residence before they arrive at Parsons Paris for their first semester. More information can be found under "What must I do before coming to Parsons Paris?"
Titre de séjour is the umbrella term for all types of French immigration documents, such as the carte de séjour, récépissé, or attestation de décision favorable. A visa is not a type of titre de séjour. Do not use those two terms interchangeably, as they are two different types of authorizations.