Yes, this definition can be a bit confusing. It is true that everyone else said, however, perhaps there is one word to better understand the system. - parallel
If you are running p1 and p2 processes on the same computer, in fact you don't need to use lamport clocks too much (maybe some extremely specific case). Instead, you can simply use the clock provided by your OS. But what if p1 and p2 are on computers that are separated by a slow and unreliable network?
Lamport assumes that you cannot trust your local clock, and you do not have the global state of the distributed system in which order events occurred on two separate computers. This is when you trigger those events that happen simultaneously.
When you debug the execution of a distributed system, and you naturally count events a3 and b3 , a3 happened before b3 . In your particular case, you are now declaring yes, but that is wrong. However, since the events are not related to each other, since they do not interact with each other, the order is usually considered parallel, and in this case it does not matter which one happened first or second for the entire system execution.
Since computers and networks are so fast and still very accurate, they are sometimes difficult to understand, let's look at the same thing a little differently:
p1 and p2 are two people living several years ago in two different valleys. They communicate together using pidgins and never talk about when they performed a specific task, only what they did. Thus, no one could know who, if a3 happened before b3 or vice versa, so they happened at the same time. Maybe not someone, the god who looked at p1 , and p2 could see it.
Unfortunately, when you have a distributed system, you cannot be a god and watch p1 and p2 at the same time, simply because messages from p1 may take longer than from p2 . Therefore, despite the fact that your monitoring system (god) received information b3 before it received information about a4 , this does not mean that they occurred in this order, it is possible that packets containing information about a4 took only longer or slower way.
After all, there is one more thing called a vector clock . Each process has clock pulses for each process in the system. The key point here is event a , which will occur only before event b , if all the hours of lamport a were less than or equal to b . If you try this with your small example, you will see that nothing happened before the others => they are parallel .