Hope as a passive wish waits quietly for circumstances to improve on their own, while hope as an active stance treats the future as something a person has some genuine role in shaping, however modest that role might actually turn out to be in any single specific situation they face.
This distinction changes behaviour directly: passive hope tends to produce waiting, while active hope tends to produce a next step, however small, taken specifically because the person believes their own effort can meaningfully move the odds in a better direction, even if only slightly. That combination of patience and consistency is, more often than not, the whole of the method.
Treated as an active stance rather than a passive feeling, hope becomes something a person can practise deliberately, choosing to act in the direction of a better outcome even without any guarantee, which is arguably the most practical and genuinely useful version of hope available to anyone.