The major difference between walking meditation and 'walking mindful' is probably that in the meditation one has nowhere to go, no destination, one just walks just up a few meters turns and walks back, with the mind focused on the steps, while walking mindful can be done anywhere, it might have a destination, a 'wanting to go', the mind is alert on everything that occurs, like stones on the path, people who come across, etc.
For both there is a time. The Buddha recommended to practice walking meditation and in some suttas it is written that he was walking up and down. It is not mandatory but recommended to do meditation sitting and walking as a set. For all the rest of the walking, wherever one goes, one should do it mindfully.
by walking and doing chores barefoot in i.e. forest monastery one trains to be mindful while walking and highly alert not to step on anything dangerous, but it is certainly different from walking meditation, when one is only with the step and has no destination, it's kind of another dimension.
Hope this is explanation is good enough.