These two terms answer different questions. Gross negligence asks how bad the carelessness was. Vicarious liability asks who has to answer for it.

Gross negligence: California's civil jury instructions (CACI No. 425) define it as the lack of any care or an extreme departure from what a reasonably careful person would do in the same situation. The measure is how far the conduct falls below the standard, not how serious the injury is. It is still not the same as intending harm, which belongs to intentional torts.

Vicarious liability: one party is held responsible for another's wrong because of their relationship. California Civil Code §2338 makes a principal responsible to third persons for an agent's negligence in the transaction of the agency's business. Example: a florist's employee runs a stop sign while making a delivery and injures a cyclist. The florist answers for the employee's negligence even though the florist was not in the van and did nothing careless.

Vicarious liability is not absolute liability. The injured cyclist must still show that the employee was negligent; the relationship only decides who else is answerable.