A collective and a cooperative are slightly different legal entities. A collective is an overarching term for any group of legal entities working together because of some shared goal or interest. A cooperative, on the other hand, is a collective specifically formed for mutual benefit, generally of an economic type, such as making money or saving money by working together.
Collectives do not, of necessity, have to be focused on economic benefit and can instead be focused on political power, for example. A cooperative can theoretically include other elements of benefit, such as social or cultural benefit in addition to economic benefit, but most often the economic benefit is the key underlying point of a cooperative and the unifying factor.
A cooperative or a collective will involve members working together to achieve their goal without a clear necessary managerial structure, meaning that each individual or entity within collectives could likely be considered on equal status and footing as all the others. This understanding of a collective also applies to a cooperative in that those individuals who are working within a cooperative are all likely on the same footing, particularly as the individuals working within a cooperative are also likely the individuals who are benefiting from the purpose of the cooperative.
Collectives and cooperatives are fundamentally controlled and owned jointly and democratically, which is part of the factors that distinguish collectives from other business organizations and entities. However, a cooperative is still technically considered a business organization.