Learn English – “Pander to” vs. “cater to”

Cooperating means working with someone in the sense of enabling: making them more able to do something (typically by providing information or resources they wouldn't otherwise have).

Collaborating means actually working alongside someone (from Latin laborare: to work) to achieve something.

The confusion comes from the overloaded meaning of "work with": In the "Work with me, people" sense, it means to go along with my idea - it's a passive condoning or suspension of disbelief rather than an active involvement. In the "I'm stuck, can you work with me on this problem?" sense it is a request for active commitment.

So in terms of helping achieve something, the ordering is something like collaboration, then cooperation, then passive indifference, then active obstruction.

Favoritism means bestows favours on, one group or person over another.

The two words are utterly different and completely unrelated.

Your "preference" simply means which one you "like more". Thus, "I prefer dogs to cats" means exactly "I like dogs more than I like cats."

The recently-coined word favoritism is utterly unrelated to "preference".

Favoritism means (particularly in a work environment) that you give favours to one person over another. Or, one (say) racial group of people over another racial group of people. Or, perhaps in a family setting, one sibling over another.

Thus for example "The Chairman exhibits favoritism (gives favours to) to people from nation XX over people from nation YY. So, people from XX get all the best promotions and all the best offices, even if they are not performing as well as people from YY."