The square root of a number is the value that multiplied by itself yields that number. For example, 4 multiplied by 4 gives 16, so 4 is a square root of 16. However, since (-4) times (-4) also equals 16, -4 is another square root of 16. Accordingly, every nonzero integer has two square roots.
On the other hand, a cube root of a number is a value which, when multiplied three times by itself, produces the number. For instance, 3 × 3 × 3 equals 27, so 3 is the cube root of 27. Unlike the square root, the cube root of a number has just one unique value, because -3 × -3 × -3 equals -27, not 27.
Hope this clarifies the distinction.