This can't possibly be MCAT-testable...
...but jod-Basedow usually occurs when there are pre-existing areas of thyroid tissue that have developed the ability for autonomous production of thyroid hormones. A sudden availability of iodine after development of these autonomous regions, say, during a period of iodine deficiency, can manifest as hyperthyroidism. Personally, I conceptualize jod-Basedow as occurring at plasma iodine levels that are sufficient for thyroid function, but not high enough to suppress function in healthy thyroid tissue, thus the problem is simply the dysfunctional areas of tissue that aren't responding properly in the long feedback loop. In thyroid storm, high-dose iodine is given (as supersaturated potassium iodide (SSKI)) because high plasma levels (i.e. higher than set can off jod-Basedow) inhibit thyroid function entirely, regardless of the normal feedback functionality of any given portion. Here, the goal is to utilize this to stop thyroid hormone production.