The two words are similar but has a slight difference in usage too. - 발(뒤)꿈치: the back part of the human foot; heel. 발꿈치가 아프다. 발꿈치가 튀어나왔다 (My heel has a protrusion). - 뒤꿈치: 1) same as 발뒤꿈치. 2) the back part of a shoe or a sock. 구두 뒤꿈치가 다 닳았다. 양말 뒤꿈치가 뚫어졌다. For the #2 meaning of 뒤꿈치, we usually don't say 발꿈치, since a shoe or sock is not a 발 (foot). The front part is called 발앞꿈치(foot) or 앞꿈치(foot, shoe, sock).

Both are virtually identical. There is even 발뒤꿈치 which also means the same.