await is used to continue execution of method body when awaiting completed. If there is nothing to continue, then you don't need awaiting.
You can think of await (simplified) as of ContinueWith operation. So, your first method is something like:
foreach (var something in someCollection)
DoSomething();
DoSomethingElse();
DoMethodAsync().ContinueWith(t => {});
There is nice MSDN article which describes what happens in async method which has nice code flow picture:
