Let's define the terms:
atom = the same thing you called variable; e.g. "x", "y", "z", etc.
literal = an atom or its negation; e.g "x" or "¬x".
clause = a disjunction of literals; e.g. (x∨y∨¬z∨w).
CNF: A formula is said to be in Conjunctive Normal Form (CNF) if it consists of AND's of several clause. For instance, (x∨y)∧(y∨¬z∨w) is a CNF formula.
The following problem is K-SAT: Given a CNF formula f, in which each clause has exactly K literals, decide whether or not f is satisfiable. That is, whether there is a an assignment to the atoms such that f evaluates to TRUE.
3-SAT and 4-SAT are the special cases of K-SAT problem.