Using a ExecutorCompletionService.poll/take, you are receiving the Futures as they finish, in completion order (more or less). Using ExecutorService.invokeAll, you do not have this power; you either block until are all completed, or you specify a timeout after which the incomplete are cancelled.
static class SleepingCallable implements Callable<String> {
  final String name;
  final long period;
  SleepingCallable(final String name, final long period) {
    this.name = name;
    this.period = period;
  }
  public String call() {
    try {
      Thread.sleep(period);
    } catch (InterruptedException ex) { }
    return name;
  }
}
Now, below I will demonstrate how invokeAll works:
final ExecutorService pool = Executors.newFixedThreadPool(2);
final List<? extends Callable<String>> callables = Arrays.asList(
    new SleepingCallable("quick", 500),
    new SleepingCallable("slow", 5000));
try {
  for (final Future<String> future : pool.invokeAll(callables)) {
    System.out.println(future.get());
  }
} catch (ExecutionException | InterruptedException ex) { }
pool.shutdown();
This produces the following output:
C:\dev\scrap>java CompletionExample
... after 5 s ...
quick
slow
Using CompletionService, we see a different output:
final ExecutorService pool = Executors.newFixedThreadPool(2);
final CompletionService<String> service = new ExecutorCompletionService<String>(pool);
final List<? extends Callable<String>> callables = Arrays.asList(
    new SleepingCallable("slow", 5000),
    new SleepingCallable("quick", 500));
for (final Callable<String> callable : callables) {
  service.submit(callable);
}
pool.shutdown();
try {
  Future<String> future;
  do {
    future = pool.isTerminated() ? service.poll() : service.take();
    if (future != null) {
      System.out.println(future.get());
    }
  } while (future != null);
} catch (ExecutionException | InterruptedException ex) { }
This produces the following output:
C:\dev\scrap>java CompletionExample
... after 500 ms ...
quick
... after 5 s ...
slow
Note the times are relative to program start, not the previous message.
Test out a working example on Replit.