What does the style of a law case contain?

Very generally, in the US the style contains only the names of the parties and a case number that shows other information (docket, year filed, case number within that year, sometimes judge assigned) Aside this generalization, it depends entirely what jurisdiction and country you are in. In the US, case styles are generally set by the state or local rules of Civil Procedure. By example, in my state,

Divorce is styled ' IN RE THE MARRIAGE OF JIM SMITH AND JANE SMITH ( not "Smith v. Smith ") followed by a case number of CF-2012-XXXX

Probate is styled "IN THE MATTER OF THE ESTATE OF JANE SMITH" PB-2012-XXXX

Suits again the state generally name an official ex relthe state, or a state agency e.g.,

JANE SMITH v. JOHN SMITH, COMMISSIONER OF PUBLIC SAFETY, EX REL THE STATE OF XXXXXXX

Child custody/guardianship cases usually use a non-oppositional styling also, and only initials for the child's name, e.g.

IN THE MATTER OF THE CUSTODY OF J.A.S

Classic torts still use the standard oppositional styling: Example:

JANE SMITH v. JOHN SMITH AUTO SALES, A CORPORATION, and JOHN SMITH, AN INDIVIDUAL.

Every state varies and the answer is usually in the state or local court rules, which are usually found in the state of local rules of Civil Procedure. Federal courts typically uses a uniform, style derived form the federal rules.

This does not mean that the cases are always CITED in the reporters (typically West in the US) in the same form. West and the Bluebook often use their own case styles when identifying a case