The distinction you’re looking for is between wildlife being contaminated with radioactive material vs the tissues of wildlife being themselves radioactive. Being contaminated involves them picking up loose radioactive contamination in the environment (typically microscopic particulates that are invisible to the naked eye). Being radioactivated requires them to be hit by a source of radiation of an extremely high energy (something like being in the core of a reactor or beside a running particle accelerator), and would afaik be fatal in extremely short order.