Thread algae, hair algae or green hair algae is most often (but not always!) a filamentous green algae (Chlorophyta). Thread algae are a quite commonly found green algae. They form carpet-like layers, growing over plants and decoration.
There are many types and forms of filamentous green algae. Very fine pale green brown strands are typically rhizoclonium genus algae:
Other forms of long green strands are typically spirogyra genus algae:
Shorter green strands can be oedogonium genus algae:
There are thousands of species of filamentous green algae and there are some filamentous species of both cyanobacteria and red algae, so the identifications above are just guesses. Each species responds to different things due to something called niche evolution. So controlling filamentous green algae is a guessing game. Here is a link to an article on controlling algae: