They are NOT the same thing! Many herbs can be useful for both culinary and medicinal applications, but the distinction between the two is very important. Culinary herbs are used to flavor foods. Medicinal herbs are used like pharmaceutical drugs; but they lack the main safety feature of standardization. That means that they are potentially toxic and seriously dangerous if used improperly!
Even standardized pharmaceutical grade herbal products that are very precisely portioned into specific doses that contain very specific rates of active ingredients have the potential to be toxic if misused, and are of course toxic to anyone who is allergic to what is being used. They must be regarded with the same sort of caution that is warranted by any other pharmaceutical medication.
Digitalis is a perfect example of a very toxic plant that is used medicinally. All parts of the plant are very poisonous! Digitalis is so toxic that it is no longer used directly as an nonstandardized and nonpharmaceutical medicinal herb. However, in a standardized pharmaceutical form, it is still sometimes prescribed for cardiac disorders. Many of us grow it just for elegantly tall flower spikes.
In our own home gardens, the strictly culinary herbs are relatively safe. Even those that can also be used medicinally are not likely used for culinary applications in quantities sufficient to be toxic. Some herbs that are used for herbal tea have more potential for toxicity, particularly if consumed regularly or excessively. Even seemingly innocuous chamomile tea, in excess, can cause nausea.
Herbs that are grown and used for medicinal applications warrant the most caution. The active ingredients as well as other chemicals in such herbs can not be accurately quantified, and are quite often variable. Doses that are measured as small volumes of plant parts might contain minimal traces of active ingredients, but could just as easily contain toxic rates. Herbalists recommend consulting with a physician prior to using any of the more potent of medicinal herbs, even if the herbs come from the garden.