However, the main difference is that if the BSGS did not find the key and finished work, then you can be sure that the key is not in the given interval. Kangaroo is a probabilistic algorithm, and you cannot be sure that there is no key in interval, even if the kangaroo has completed the estimated number of operations.
That's true, but:
1) I would rather say the biggest difference is in resources needed, as BSGS requires much more memory
2) Kangaroo is "probabilistic", but with a big enough amount of work done, the chances for a final result are very close to 100%. That's well described on JLP program's page.