What's the difference between chutney and relish?
It depends on what cuisine it is, though all chutneys and relishes are used as condiments/sides. In European cuisine, chutneys tend to be jammier and involve fruit of some kind. Relishes, like Elendil mentions, are usually made from pickled vegetables. As far as I have experienced, the chutney moniker is used when non traditional ingredients are involved Mango chutney, ginger mint chutney) whereas a relish is used when it is made from slightly more familiar ingredients like dill, cucumber etc (This is with regard to non Indian cuisine).

In Indian cuisine (which is where the chutney moniker originated from), chutneys are thinner and are almost always  savory, even when they involve a fruit(eg., mango chutney will have chillies and salt in it). Indian chutneys involve herbs and chillies and sometimes even nuts/lentils. The texture difference comes from the fact that it is usually blended/pureed and usually water based. But then again, you would not have landed in this situation if the meal was Indian, as there is no concept of a relish there.