There are basically two types of contracts between a service provider and a client :-
Service Contract : Also sometimes referred as service-level agreement (SLA) is an agreement in which the level of service is formally defined. In practice, the term SLA is sometimes used to refer to the contracted delivery time (of the service) or performance. As an example, software providers will commonly include service level agreements within the terms of their contracts with customers to define the level(s) of service/product being provided in plain language terms.
Non-Disclosure Agreement(NDA) (This is optional) confidentiality agreement (CA), confidential disclosure agreement (CDA), proprietary information agreement (PIA), or secrecy agreement, is a legal contract between at least two parties that outlines confidential material, knowledge, or information that the parties wish to share with one another for certain purposes, but wish to restrict access to or by third parties.