If you can't tell the difference between two things, they're indistinguishable — they appear the same. Although their parents can tell them apart, identical twins are indistinguishable to most people.
It's easy to see which of two bills is worth twenty dollars and which is Monopoly money, but a professionally counterfeited bill is indistinguishable from a real one. One of the earliest uses of this word was by Shakespeare around 1600, when he gave it the meaning "of indeterminate shape." The definition evolved, first to "not clearly perceived," and then finally to "incapable of being told apart."