Cooperating businesses are working on the same project, it's a form of first date.
Cooperation means literally operating together, the process of working together to the same end, Collaboration is stronger than that, the action of working with someone to produce or create something together. When a business cooperates with another, it means they understand the other parties objective and do things to help them achieve it. A supplier my be cooperating with your business for example by meeting out of hours delivery times or by providing a bespoke product. The measure is in the fee he charges not in the value he creates for you.
In cooperating environments things tend to change in only one organisation. 
The organisations work independently on the same project.
When we collaborate both organisations change. Sometimes significantly. Collaborating organisations look out for each other - they don't work independently but interdependently.
It's people and relationships.
Collaborating is like long term dating, it's like a couple who have moved beyond meeting and chatting in Social Conversation, and doing more than sharing experiences in Social Cooperation, perhaps agreeing to meet tomorrow evening and go out, but not doing much to help the other party until then. There comes a time when people reorganise their lives around a common purpose and shared goal, they collaborate on the other things they do, the things just one party needs and wants as well as the things they do together. Perhaps they get engaged.
Do be too fast.
One real challenge for many businesses is they see the opportunity to collaborate long before the parties are emotionally ready to do so. Just like dating, if the offer is made before the other part is ready, before there is trust and desire, the advance is likely to be rejected. Collaboration is about both parties, so take your time, it could just last a lifetime.
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