To me, they often go hand in hand. A person is considered popular because they're well known across the community. Being well known then helps you become popular - everybody will then want to talk to and get to know you.
I agree with what you say if only because of the leverage in the bolded word. However I think you are misunderstanding the underlying relationship between being well known and being popular. Let me break it down for you. Consider the following.
Statement A: I am well known.
Statement B: I am popular.
The relation between these two statements is as follows.
B => A
In English this means the following.
If I am popular then I am well known.
What you are suggesting is.
B <=> A
Which isn't true in a consistent sense and let me tell you why. If someone is popular, then they
must be well known. That is absolutely logically justified. However if someone is well known, then that (strictly speaking) does not
necessarily make them popular. For example would you consider a well known criminal to be popular?
That being said I am willing to agree that the two can often have the relationship B <=> A but remember, this is not strictly true / true for all cases.