In seti@home, they are all being controlled from a single location to work on a single task, while the entire internet consists of independent machines operated

In seti@home, they are all being controlled from a single location to work on a single task, while the entire internet consists of independent machines operated independently. That's what allows you to talk about seti@home as a single supercomputer, even though it's somewhat tenuous as the problem is so embarrassingly parallel, it would never compete on any actual supercomputer benchmarks which require low-latency communication between nodes.