How multiple consumer group consumers work across partition on the same topic in Kafka?

Yes they get the same data. Kafka only stores one copy of the data in the topic partitions' commit log. If consumers are not in the same group then they can each get the same data using fetch requests from the clients' consumer library. The assignment of which partitions each group member will get is managed by the lead consumer of each group. The entire process in detailed steps is documented here https://community.hortonworks.com/articles/72378/understanding-kafka-consumer-partition-assignment.html

Offsets are "managed" by the consumers, but "stored" in a special __consumer_offsets topic on the Kafka brokers.

Offsets are stored for each (consumer group, topic, partition) tuple. This combination is also used as the key when publishing offsets to the __consumer_offsets topic so that log compaction can delete old unneeded offset commit messages and so that all offsets for the same (consumer group, topic, partition) tuple are stored in the same partition of the __consumer_offsets topic (which defaults to 50 partitions)