Nexus is not a tax but rather the minimum link or connection to a state that is necessary before a state can force you to pay its taxes or collect taxes on its behalf. There are different nexus rules for income tax and sales tax. If you have nexus with a state for sales tax your next step would be to determine if what you sell or do in that state is taxable.

Affiliate Nexus can refer to two different types of activities. The original meaning referred to the relationship between related entities and how the activities of one company could create nexus for the other. More recently affiliate nexus is often related to online affiliates. An online affiliate is a third party website that directs customers to another website by way of a link in return for a commission or fee if a purchase is subsequently made. This is also called “click through” nexus. How states look at affiliate nexus varies widely from state to state.

I would add that if you think you may owe tax to another state based on your business activities in that state (for income tax or sales/use tax purposes), contact the state's taxing agencies or a practitioner in that state to determine whether the state has any voluntary disclosure/amnesty program at this time. Many states offer some type of relief, either through limited or eliminated tax penalties, or a reduction of prior years reviewed, to taxpayers who come forward voluntarily to come into compliance. The benefits of these programs can be significant, particularly in California.