You and a buddy want to operate a business, and both of you want to save some money. You're both informal people eager to get on with business, so both of you simply start selling stuff.
You've just entered into a partnership with your buddy. As partners, each of you is liable to the full extent of your personal assets for the debts and other liabilities of the partnership business.
That sounds scary, but a partnership is not automatically a bad thing. Depending on the particular circumstances, a partnership may be the best way to do business because the law may not allow you to incorporate. For example, many investment funds operate as a partnership, and some law firms operate a special form of partnership as well.
What is important is that both of you know that you've created a partnership, and that both of you wanted it to be that way.
A partnership may be created even without an express partnership agreement. Whether a partnership exists is determined objectively by a court.
In fact, an express provision in a written agreement denying that the you and your buddy are NOT partners may not be conclusive proof in showing that a partnership does not exist.
The best way to show that you're not in a partnership? Incorporate.