Where is offset of consumer stored in Kafka

Question

In Kafka, I know that there is a topic, named __consumer_offsets, which is used to store the offsets of consumers. As my understanding, a consumer will do two kinds of things:

1. fetch data from partition.
2. write the offsets to the topic __consumer_offsets.

After reading this link: https://www.learningjournal.guru/courses/kafka/kafka-foundation-training/offset-management/, I knew that there were two kinds of offsets for a Kafka consumer: the current offset and the committed offset.

I've read many docs and blogs of Kafka, but it seems that all descriptions about offsets of consumer are about the committed offset. For example, enable.auto.commit=true will make the consumer write the committed offset to the topic __consumer_offsets automatically and the function commitSync() can manually write the committed offset to the topic __consumer_offsets.

Now I want to know how Kafka processes the current offset. Will it be write into the topic __consumer_offsets too? How? When?