A risk neutral party's decisions are not affected by the degree of uncertainty in a set of outcomes, so a risk neutral party is indifferent between choices with equal expected payoffs even if one choice is riskier.
In the context of the theory of the firm, a risk neutral firm facing risk about the market price of its product, and caring only about profit, would maximize the expected value of its profit (with respect to its choices of labor input usage, output produced, etc.).
But a risk averse firm in the same environment would typically take a more cautious approach.
In contrast, a risk averse investor would diversify among a variety of assets, taking account of their risk features, even though doing so would lower the expected return on the overall portfolio.
Utility is often assumed to be a function of profit or final portfolio wealth, with a positive first derivative.