Kafka consumer - what's the relation of consumer processes and threads with topic partitions

I have been working with Kafka lately and have bit of confusion regarding the consumers under a consumer group. The center of the confusion is whether to implement consumers as processes or threads. For this question, assume I am using the high level consumer.

Let's consider a scenario that I have experimented with. In my topic there are 2 partitions (for simplicity let's assume replication factor is just 1). I created a consumer (ConsumerConnector) process consumer1 with group group1, then created a topic count map of size 2 and then spawned 2 consumer threads consumer1_thread1 and consumer1_thread2 under that process. It looks like consumer1_thread1 is consuming partition 0 and consumer1_thread2 is consuming partition 1. Is this behaviour always deterministic? Below is the code snippet. Class TestConsumer is my consumer thread class.

    ...
    Map<String, Integer> topicCountMap = new HashMap<String, Integer>();
    topicCountMap.put(topic, new Integer(2));
    Map<String, List<KafkaStream<byte[], byte[]>>> consumerMap = consumer.createMessageStreams(topicCountMap);
    List<KafkaStream<byte[], byte[]>> streams = consumerMap.get(topic);

    executor = Executors.newFixedThreadPool(2);

    int threadNumber = 0;
    for (final KafkaStream stream : streams) {
        executor.submit(new TestConsumer(stream, threadNumber));
        threadNumber++;
    }
    ...

Now, let's consider another scenario (which I haven't experimented but am curious) where I start 2 consumer processes consumer1 and consumer2 both having the same group group1 and each of them is a single threaded process. Now my questions are:

1. How will the two independent consumer processes (under the same group nevertheless) be related to the partitions in this case ? How is it different from the above single process multi-thread scenario?

2. In general, how are consumer threads or processes mapped / related to partitions in the topic?

3. The Kafka documentation does say that each consumer under a consumer group will consume one partition. However, does that refer to a consumer thread (like my above code example) or independent consumer processes?

4. Is there any subtle thing I am missing here regarding implementing consumers as processes vs threads? Thanks in advance.