These are distinct senses of "random". Pi is conjectured (but not proven) to be a so-called normal number, which means that n-grams have uniform frequencies, so if you slide a window of size n over the digits, then every sequence of n digits will come up with equal frequency in the limit.
Chaitin's omega is "random" in a stronger sense. There is no finite algorithm that can produce the digits. There's no compact, finite representation from which you could "unpack" those digits. The digits are what they are, the best way to represent them is simply to list them.
Pi's digits are very "regular", but the pattern is not about repetitions in digits or skewed frequencies of certain digit sequences but that the digits follow from simple rules. A short program can generate those digits to arbitrary length. So in some sense they have redundancy, a kind of pattern to them.
Chaitin's omega is "random" in a stronger sense. There is no finite algorithm that can produce the digits. There's no compact, finite representation from which you could "unpack" those digits. The digits are what they are, the best way to represent them is simply to list them.
Pi's digits are very "regular", but the pattern is not about repetitions in digits or skewed frequencies of certain digit sequences but that the digits follow from simple rules. A short program can generate those digits to arbitrary length. So in some sense they have redundancy, a kind of pattern to them.