Jacuzzi is actually a brand name whereas whirlpool is a generic name. The Jacuzzi company specializes in whirlpools (source). In the 1950s, a man called “Jacuzzi” popularized what we now know as a spa bath or a whirlpool.
There is little or no difference between a jacuzzi tub and a whirlpool. The terms are often used interchangeably to describe an oversized tub that is attached to a pump system, which then propels water and air through jets. This creates a “whirlpool effect” or hydro massage.