Both are general purpose languages, so of course they overlap.
> Good luck rewritting all the big data tools from Java (Elasticsearch, Spark, Kafka, Hadoop, Neo4j, Deeplearning4j, Cassandra, Solr, Arrow, OrientDB)
Cassandra (https://scylladb.com) and Kafka (https://vectorized.io) have already been rewritten once in C++, with massive latency and throughput improvements. No reason why they couldn't get their superior Rust clones in the observable future.
Materialize (https://materialize.com), Noria (https://github.com/mit-pdos/noria), and Sled (https://github.com/spacejam/sled) are just some of the Rust database projects that are aiming at unseating the de facto standard implementations in the space. InfluxDB (https://www.influxdata.com) is now doing major Rust development as well.
The future is almost here. It's just not evenly distributed yet.