Thats razor/scissor caulerpa. Not chaeto. Chaetomorpha is the string/hair like algae that is usually found in clumps. It doesnt attach with a root system like the other algae.
When I started in the reef hobby I thought it would be cool to get algae to grow on my rocks. I intentionally attached it all over my rock work. Needless to say, that turned into a disaster. The grape caulerpa went a sexual and the razor caulerpa spread like wild fire. I was forced to break down my tank and scrub each rock to get the stuff off.
