If you look around, you'll find a lot of disagreement on what, exactly, concurrency and parallelism are. You'll have to define them for your purposes before being able to give examples.
Concurrency is sometimes defined as multiple tasks whose order doesn't matter (so A can run before B, or B can run before A, without causing a problem). However, there is sometimes also the caveat that A and B must be working toward a common goal.
Parallelism is typically defined as two tasks running at the same time, such as with two processors or two separate computers. However, parallelism is also often thought of in terms of working toward a common goal, so the fact that two separate programs can execute simultaneously on a multiprocessor machine might not really be parallelism, because they have nothing to do with each other.
So, depending on the definitions, it may be impossible to have parallelism without concurrency, as (by those definitions) parallelism implies concurrency. Once you've got concrete definitions for concurrency and parallelism, then you can figure out what the examples should look like.
If I were explaining this in an Erlang tutorial, I'd probably avoid mentioning concurrency and parallelism entirely, just because it's so muddled. I'd say that Erlang has processes which work independently of each other, but which can communicate via message passing. If the hardware supports it, or if multiple Erlang nodes are in use, these processes might actually run simultaneously. Otherwise, Erlang schedules them to appear to run simultaneously, as far as we're concerned. This covers the broad ideas of concurrency and parallelism, hoperfully without worrying about pointless bickering over definitions
Note: The above sample definitions of concurrency and parallelism are not meant to be exhaustive or authoritative. They're merely for illustrative purposes.
