A pull-up bar is a horizontally fixed bar that allows for exercises such as pull-ups (hence the name), chin-ups, leg raises, windshield wipers, etc. A power rack, on the other hand, is much more complex. Power racks have a pull-up bar as part of their construction allowing for all the above listed exercises.
On a power rack, you can do exercises that you simply can’t do on a pull-up bar (e.g., barbell squats, bench press, barbell lunges, rack pulls, etc.). A power rack is bigger, more costly, more versatile and more complex than a pull-up bar.