They are separate genera and species from the same family, Brassicaceae, informally known as the mustards, mustard flowers, the crucifers, cruciferous vegetables or the cabbage family.
The family contains well-known species such as Brassica oleracea (broccoli, cabbage, cauliflower, kale, collards, Brussels sprouts, etc.), Brassica rapa (turnip, mizuna, napa cabbage, etc.), Brassica napus (canola, etc.), Raphanus sativus (common radish), Armoracia rusticana(horseradish), and many others.
Horseradish its a root, that grows in the ground. You can use it to make paste. (Some countries believe it's really good for your throat.) It has a very strong taste. It's used to make a sauce or in pickles.
The common radish is also a root vegetable. It has similar taste to horseradish, but not as strong. Some radishes are white and long (around 10-15 cm); others are small pink balls. It's very healthy. Just slice it and put on sandwich or use for salads.
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Potato contains starch whereas radish don’t.
You can search if radish/potato has starch