There are many different styles of cardio to stimulate your body to change in one way or another. Here are a few examples:

A fairly fit young person wants to lose fat and preserve muscle mass - high intensity interval training would be very appropriate (all-out interval sprints).

An older person wants to improve their general health - a lower intensity and longer duration low-impact cardio would be appropriate.

A person is training for a 10km run - get them to do 10km runs.

Someone has a poor level of fitness and wants to burn body fat - begin with longer low-intensity cardio and gradually build up their fitness by increasing the intensity (and thus burning more fat).

Those examples that you mentioned with the zone's are old-school mentality. You have a fat-burning zone (low-medium intensity) and a cardio zone (medium-high intensity). Whilst a lower intensity will burn more fat during the workout itself, a higher intensity will turn the body into a fat-burning machine for up to 24 hours after the workout has completed. It's like supercharging your metabolism. This results in up to 9x more fat being broken down. But at the same time - it's not appropriate for everyone.

Here are a couple of articles I have on the topic:

The Fat Burning Zone
Myths Under the Microscope - Fat Burning Zone

The first I wrote for a few popular magazines and are targeted to the general population. The second article has a lot of scientific jargon contained within.