Here's the difference between Apollo 11 and Saturn V:
Apollo 11 was the name for that particular mission to take those astronauts to the moon. There had been a few Apollo missions before this one, but Apollo 11 was the first one to take astronauts to the moon, and bring them back. The term "Apollo 11" also refers to the particular spacecraft that was used to do this.
It's important to remember that the rocket itself didn't get to the moon- what happened was that they put the Apollo spacecraft on top of a Saturn V rocket. The rocket was used to get it into orbit. From orbit, it detached from the rocket and then went to the moon and back.
Saturn V was the particular type of rocket that was used to get the Apollo spacecraft, not any one specific rocket. Like many vehicles, rockets are usually manufactured in various types, and a manufacturer will often make several rockets of the same type. Usually, each particular family of rockets and particular rocket types within that family, gets its own name. There were 13 Saturn V rockets that were launched. As far as I know, the Saturn V rockets didn't all get individual names, even though the Apollo spacecraft they launched did.
So basically, a Saturn V rocket was used to take the Apollo 11 spacecraft into space, and from there, Apollo 11 left the Saturn V rocket behind and went to the moon.
Later on, a new Saturn V rocket was used to take Apollo 12 into space, and Apollo 12 also left its Saturn V rocket behind to go to the moon, and so forth. Each Apollo mission got its own Saturn V rocket to get into space, and from there, it went to the moon.
They also used a few Saturn V rockets for testing, and one of them was used to launch the Skylab space station into space as well.
For interest, the Saturn V was the most powerful rocket type ever made; no rocket since then has ever been as powerful (mostly as they no longer need to launch heavy missions with all the equipment and fuel needed to get astronauts to the moon and back). However, some even more powerful rockets are once again under development for a potential Mars mission.