A co-operative is owned and run jointly by its members, all of whom share equal status. Each owns an equal share and has an equal voice in the business. Outsiders may not own a share.
A co-operative will use its profit as a bonus for members, for the good of the community, or retain it in the business for expansion.
Co-operatives enjoy limited liability, although to get bank loans personal guarantees may be required. Since outsiders may not hold shares, co-operatives cannot raise equity finance, except to the limit of what each member can invest personally.
Industrial Common Ownership Finance (ICOF) can provide loan finance for co-operatives - see the link below.
If you are interested in the principles of a co-operative but are unsure about establishing such an organisation, there is no reason why you could not start trading as a partnership, but adhere to co-operative principles and practices.