What is the difference between "dikaryotic" and "heterokaryotic" states in the sexual lifecyles of fungi?
A heterokaryon is a fungal cell which has two or more genetically-distinct but allelically-compatible nuclei, as suggested by this resource, as well as this Wikipedia article. 

A dikaryon is a fungal cell which has precisely two genetically-distinct but allelically-compatible nuclei, as shown here and here.

In this sense,  a heterokaryon is a general term, whereas a dikaryon is a specific term. A dikaryon and a trikaryon (although not often seen in literature) are both heterokaryons.