For the most part it is just contamination with radioactive particles. The tool used to remove the fuel rods will pick up some surface contamination. If its Uranium that’s not too bad because it decays slow, if its contaminated with some of the fission products it’ll be a lot more radioactive for a bit
That said, metals in the reactor itself can become radioactive. Both fission and fusion produce high speed neutrons which can strike an atom and join with it, this is called [Neutron activation](https://en.wikipedia.org/wiki/Neutron_activation). Basically all iron that you can find is stable, but if you start smacking it with neutrons then some of that 5% that is Fe-54 becomes Fe-55 which is radioactive with a 2 year half life so you will have taken non-radioactive steel and made radioactive steel
For it to matter you need to be hitting it with a lot of neutrons to create a lot of Fe-55 so a steel liner of a reactor may have issues after decades but an iron hammer that gets near a fission reactor won’t have any notable changes
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