What is the difference from Passive loss rules to at risk rules?

First and foremost, both of these terms are tax terms of art. Passive losses are "hobby losses," losses that are not derived from the main business activity. These losses are sometimes deductible. In contrast, the "at risk rules" is basically an understanding used in partnership, which states that you cannot allocated losses to someone not at risk for those losses; thus, you must allocated loss by the amount of risk, which is usually also demonstrated by gain allocation. E.g. A partnership has three partners, A, B, and C. A and B each put in 49% of the income, C puts in 2%. That year the partnership has 100 dollars in losses. The partnership cannot allocate 100% of the losses to C, because he was not "at risk" of losing that much. These rules were enacted to do away with tax shelters that throw out losses to investors.