As soon as you offer to employ someone, and that offer is accepted there is an employment contract. The contract should ideally be in writing, but can be verbal or implied.
A contract, whether written, verbal or implied is a formal agreement between you, the employer, and your employee. The contract sets out the employment conditions, rights, responsibilities and duties of both the employee and employer.
Not all people that undertake work for you will be employees, you may subcontract certain tasks or use self employed ‘consultants’, this isn’t an employment contract but a ‘contract to provide services’.
The employment conditions, rights and duties etc, are the ‘terms’ of the contract and the parties must comply with these terms otherwise they will breach the contract. Terms can be changed usually with the agreement of both parties.