This is a somewhat imprecise question because all of these are legal requirements that have an impact on the administration of human resources. It is probably a good idea to sort out the difference between a law and a regulation before we talk about any specifics in either.
A law, generally called a statute, is enacted by a legislature, either state or federal. A regulation is enacted by an agency, but only pursuant to what is called an enabling statute, one that gives the agency authority to enact regulations regarding a particular statue. Safety is an area in which there can be statutes and regulations, at both the federal and state level.
Some laws that have an impact on human resources work are anti-discrimination statutes, worker's compensation statutes, and unemployment compensation statutes, each having its own body of regulations. Simply put, their effect upon the human resources process is that human resources administrators must be sure that the workplace is in compliance with all statutes and regulations in these areas of law.
For anti-discrimination statutes and regulations, both state and federal, human resources people must be sure that they do not recruit, hire, promote, or terminate people based upon their protected classes. They must also be sure that they accommodate people with disabilities, as long as the disabled can do the essential functions of their job. Part of the body of law in this area means keeping the workplace free of sexual harassment, too.
Workers' compensation statutes and regulations, which are state laws, must be complied with, so that workers who are injured on the job receive compensation and medical care. Human resources people must determine whether or not an injured worker can return to a light duty job and prepare to take back the employee who is cleared to return to the workplace.
Unemployment compensation statutes and regulations, which are also a function of state law, provide for unemployment compensation for the loss of a job when it is not the employee's fault. Human resources people make a determination as to fault or no fault, so they can oppose unemployment compensation claims if need be.
As far as safety is concerned, there are federal and state laws and regulations on safety in the workplace. The Occupational Safety and Health Administration (OSHA) is the agency that most people are familiar with, a federal agency that administers over the health and safety statute and regulations. Human resources departments are responsible for seeing to it that the workplace is in compliance with all statutes and regulations regarding employee safety. In a medical setting, for example, healthcare workers are frequently required to wear masks and gloves. Another example is a construction site, where workers need hard hats and steel-toed boots as protection. It is human resources that makes sure that these protections are in place.
For a human resource department, there are literally hundreds of statutes and regulations that effect the daily work of the department. These are just a few, and it would take a book to discuss all of them! The important thing to understand is that human resources people must be very well versed in the law.