It has been a long time since I played a game of GUMSHOE, so I'll try my best. Both of these types of actions involve more than one character, more than one performer of the deed. As you've understood the mechanical difference, let's move to the conceptual one.
A piggybacking is an action in which someone performs a deed and all of the other characters enjoy the benefit. An example for this kind of action will be moving without being seen. Some of us are better with it than others; some of the PCs have invisibility powers and the like.
Let's imagine a scene: the PCs try to infiltrate into a warehouse without being noticed. Being good in hiding can let me go in there without being noticed. But maybe I'm not, maybe I can't move silently enough, or disappear or whatever. So I need help. Here comes the piggybacking to the rescue. It lets the amazing Glinda to guide us through the secret passages, to make us hide where there are shadows and where the cameras don't look.
Piggybacking is more for the types of actions when there is one who knows how to do something and the others don't. Thus, this lets him/her to help all the others to get to a certain point, to not get noticed…
In this type of action we have two people who try to achieve something, but more than that- they try to achieve this while both of them can act and help in order to achieve this goal.
Let's imagine another scene: Glinda and Rob try to find clues in the destroyed warehouse. Glinda uses her super-strength in order to lift things and see what lies beneath them, while Rob uses his X-ray vision in order to see through other things. As both of them can act and help each other to achieve the goal, to find the clue, it is a cooperative action.
I know that finding clues uses a different mechanic, but for the sake of example it works. It can also be saving someone or something, if it helps.
Cooperation, thus, is used when all of the participants can help to achieve the goal.
Piggybacking vs. Cooperation
As a rule of thumb, piggybacking is used whenever only a certain character can take the action. Only one can guide the group when they try to sneak into the guarded warehouse, so it is piggybacking.
Cooperation is used when both parties can cooperate to achieve the goal. One can lift while the other sees; one can dig while the other looks for clues in the sky.