Generally a remedy at law would be monetary damages. A remedy in equity is based on the idea of fairness. There are not distinct courts for either as all courts can apply both.
Check this out: http://en.wikipedia.org/wiki/Equitable_remedies
Years ago there were courts at equity and courts at law. In recent years and in most jurisdictions courts will hear both actions in equity and actions in law. An action at law is an action typically for money damages such as a tort (personal injury or medical malpractice action) or breach of contract action. An action in equity seeks a remedy when there is no available remedy at law. For instance, if money damages will not suffice. An example of an equitable action is specific performance in a sale of property or a house. In this action, the plaintiff will ask the court to make the owner go through with the purchase because houses or property are unique.
I hope this helps.
I am not licensed in CA, but am licensed in TN and FL. I only actively practice in Florida currently. When I was practicing in TN there were separate courts as you have suggested. It was very interesting because the courts of equity were called Chancery courts. When a divorce or custody case was filed the clerk would reach into a bin and draw out a cube labeled chancery or circuit. Traditionally courts of equity provide remedies related to performance of an obligation as opposed to compensatory remedies like money. Today, most states do not separate the courts by the remedy available. All circuit courts can provide the remedy sought and proven.