It stems from the fact that Japan invented emojis (it is in fact a very Japanese sounding word) and they eat sweet potatoes much more often than the other kind you're mentioning. Just wanted to make the oversight a little less bizarre for you.
Weird. I must be mistaken; the last time I searched for a potato emoji, it only brought up sweet potato. Perhaps that app was using an older version of the standard; I don't remember for sure.