Hoping to support @Rustler's response with some additional information:
The reason a partner in a partnership ( not to be confused with partners within a corporation) is not an employee has to do with the way that taxes are reported. Much like sole-proprietors, all income/losses are "passed-through" to their tax returns. At the end of the year your total income is used to calculate your self-employed tax.
Alternatively, it is possible to structure different business entities like an Limited Liability Corporation or an S-Corporation that are based on a partnership ( multiple people collectively owning the entity) at which time it may require you to setup a payroll. Some LLC's can elect to file as a S-Corp for tax purposes. Once you file as a corporation, the corporation will file its own tax return and then each involved party will report their own wages and profits earned from the corporation on their own individual returns.
Full Disclosure: Please note that I am not an enrolled agent or a CPA, and I always advise that you speak with your tax professional or attorney before deciding entity types. I hope this information helps provide you additional knowledge while you continue your research. .