Long-lived high-level nuclear waste, colloquially known as nuclear waste, as in "but what do you do with the waste" IS spent nuclear fuel. There's also low-level rad waste that goes in special landfills but no one worries too much about that.

This is fission products, actinides, and uranium-238.

[1] https://en.wikipedia.org/wiki/Radioactive_waste#High-level_w...