Below, if you pull up a stem, you can easily see that it's a low growing vine.
Working with many new gardeners, I find that it's not uncommon for people to confuse the two, at least until they're grown them both. The differences then are really obvious. The two plants don't look anything alike. Their growth habit is different. The tubers even look different. Their flavor is different that even the non-sweet varieties of the sweet potato won't be mistaken for an Irish potato.
So after one more rambling post about sweet potatoes, I'll move in the potatoes and hopefully lift the cloud of confusion I've caused around "D". But first, some comparisons.......
...vining growth habit
...tubers develop as an enlargement along the root, thus there is a root coming into the tuber and a root leaving the other end of the tuber
...leaves are edible
...tuber skins may be white, tan, orange, pink, red, purple
...flesh may be white, creamy, light yellow, pale orange, bright orange, reddish orange, light violet ranging to deep dark purple. Streaks and blotches of contrasting colors is not uncommon.
...tubers generally mature around 5 months
...flavor is general sweet to some degree
...bush growth habit
...tubers develop at the end of a rootlike stem or along the underground stem
...leaves are not edible
...tuber skins may be white, tan, brown, pink, red, dark purple. May be blotched.
...flesh may be white, pale gold, medium gold, pink, light reddish, bluish, purple. Streaking of pink, red, or blue may occur on white or whitish flesh.
...tubers generally mature around 3 months
...flavor is generally somewhat nutty, but not sweet
Above, a very young potato. It's attached to the plant via one rootlike stem.
Below, a young sweet potato. Usually a thick stem-like root coming to the tuber on one end and a thinner one going out the other end.