A titre de séjour is literally something that allows you to stay in France. It's a legal concept and the title of a chapter in the Code de l'entrée et du séjour des étrangers et du droit d'asile. A carte de séjour is a specific document and a type of titre de séjour but there are others, like the carte de résident. In practice, it will say “Titre de séjour” on the top of the document with the specific type down below, under the heading “Nature du titre”.
Roughly, a carte de séjour is a 1 to 3-year renewable residence permit and a carte de résident is a long-term or permanent residence permit but there are many different types of carte de séjour and a bunch of other special documents (autorisation provisoire de séjour, récépissé of an application or renewal of another document, etc.)
Once you have a carte de séjour, you don't need a visa anymore, the carte de séjour replaces it. Unlike the US for example, France does not require you to have a visa to (re)enter the country if you have a residence permit. Schengen countries also have similar rules and honour other Schengen residence permit so you can use your French residence permit to reenter through another country.
Typically, new residents enter France with a long-stay visa valid for one year and then secure a carte de séjour which they renew regularly. After that point, they don't need a visa anymore. But a long-stay visa need not be valid for one year, that's only the maximum. It can have any validity between three months (the threshold for short-stay visas) and one year.
In any case, the carte de séjour is valid until the date that's printed on it, unless the préfecture explicitely cancels it. Unlike many other countries, France does not have residence permits that implicitly lose their validity based on some external condition like losing your job. So the conclusion of all this is that you can have to go by the date printed on the last titre de séjour you got (whether it's a visa or card).