The word refers to not only the relation between the two parties but at the same time in the US, Employment Status is referred to as the basis for the identification of the contract between the two. The contacts such as,
Employment at will : This is routine most contract types practiced in the US, whereby both the parties can terminate the job at any time without assigning any notice periods by either party to the other. But at the same time employer can never terminate employees on a false basis like color, creed, class, family, discrimination or counter-attack, etc.
Employment based on writing agreement: Here, it is featured as an in detail contract covering therein the terms and conditions for both the parties i.e. employer as well as the (to-be) employee. It routinely encompasses a certain period of time mentioned decided by the employer side on need basis of some projects completion/time period tasks etc. like in powerhouses the shutdowns need few more employees to be hired for a certain period of time covering and completing shut down repairs jobs, they are also called as on contingent based employees. The employers, upon violation of rules by the employees, may terminate such contracts.
Oral based contracts for the job: The legal contract these are, but with limited evidence of some surrounded environment like if any paper or a person as evidence is used in case of any dispute between the parties (say employer and the employee). Thereupon either evidence or the reputation of the party is given weightage for resolving disputes if any. Otherwise, these contracts can be either time bound like written ones or the at will job contracts categorically.
Implied Oral Job contracts: This sort of job contract can be a mix of both oral and written and have no documents in a formal way. In case of any dispute solver, the courts of Law look into the matters of the employee tenures and their performance with the organizations, for taking any decision.
Too, in several other countries: the employees either they are full time job workers, part timers, contingency based, or self employed contractors are also defined through the employee status. But in the US routinely Internal Revenue Service (IRS) does not discriminate on the rights of the employees on the basis of employment status rather they call workers either employees or nonemployees (self-employed out workers/independent contractors/freelancers/service providers/suppliers).
Related: Employment at Will