These forms of iodine are quite distinct from one another and some are most definitely toxic! Tincture of iodine is made with alcohol. Do not drink it! Radioactive iodine is used to kill a thyroid gland for some (sometimes dubious) medical procedures...avoid it! Povidone iodine is used as a disinfectant...don't drink that either!
I have yet to read of a case of Lugol's poisoning. If anyone knows of a documented case, please let me know.
BTW Lugol's can also be used as a disinfectant. It has been used since its discovery to disinfect water. It can also be used topically, although you will look yellow for a while.