People often use these three terms interchangeably but there are slight differences.
A VISA VLS-TS is a conditional authorization granted to a foreign student to legally enter, remain and leave / come back into France for the duration of the visa. A visa is the sticker-like document placed in your passport that indicates the status you hold. Most students are given a VLS-TS 'étudiant' visa. A VLS-TS is a visa that is valid for longer than 4 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 European Union, you need a French student visa to both legally enter and to study in France for longer than 3 months.
A carte de séjour is a type of residence permit, or temporary identity card, that is the size of a debit/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 longer than 3 months in order to study. Other students and people you meet may have a carte with a different status, such as spouse, working, refugee, etc. Please know that you will not 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 procure a student visa depending on the type of residence permit they were granted. Please make sure to speak with API, Academic Programs International, who help students procure 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.'
A titre de séjour is the umbrella term for all the different types of French immigration documents such as carte de séjours, récépisses, attestation de décision favorable, etc. that gives the holder the legal status to remain and live in France.