Consider two processes that share a resource. They use this shared resource to communicate with each other. This resource could be a shared variable or it could be a shared message channel.
The essence of concurrency is synchronizing access to the shared resource. In the extreme, if two processes are running concurrently and do not share any resource then they cannot communicate with each other; thus, they have no reason (or need) to synchronize with each other. They don't even have any reason to know about each other. Things only get interesting if the two processes want to exchange some information, i.e., communicate with each other.
If the shared resource is a shared variable, then presumably after one process, P, writes a value to the variable the other process, Q, can read it; in this indirect manner, P communicates with Q. It's like agreeing with your friend (whom your parents forbid you to see) that you'll secretly leave each other notes under a rock to communicate. This means of communication brings up the issue of synchronization since only one person at a time can be at the rock.
If the shared resource is a shared message channel, P can send a message directly to Q. The channel is the medium through which the message travels. This means of communication brings up issues like transmission delay (it takes time for messages to travel), buffering (suppose Q is busy reading the last message P sent it?), ordering (are messages received in the same order sent?), duplicates (are duplicate messages allowed?), lossiness (what happens if a message is lost?), and failures (what happens if the channel breaks?).
Which one of the these models, shared-memory or message-passing, you choose to describe your concurrent system depends on the features of the system you want to focus on, the kind of reasoning you want to perform, or simply your taste, preference, or familiarity. Theoreticians have shown that you can always model one in terms of the other so you are not losing or gaining any expressive power by choosing one over the other.