Eva, I think the key to this, instead of trying to define them
distinctively against each other as to what one is and what one isn't since the boundaries do run into each other, is to remember the etomology of the words themselves. They're basically condiments.
Relish began as a French condiment.
Chutney began as an Indian condiment.
Salsa began as a Spanish condiment.
And since then, in this modern world, they've all been put into the blender and whirled around. So it is quite possible and reasonable to find that what one calls a salsa in one cuisine could quite correctly be called a chutney or relish in another.
There are, of course, cuisine indicative clues to the origin of one or the other to guide in the naming.
This reminds me of a story of my grandmother. She was a basic German-Southern style cook (meaning she cooked a lot of dishes from her Germanic background combined with the southern US style of cooking). While it was wonderful food, there wasn't too much spicy going on. Her spices were salt and pepper and the flavor of the food. However, she made this wicked "mango relish" (mango being what her generation called a green bell pepper) that would send flames out your ears. She used it to perk up roasts and especially bean dishes. She basically took every hot pepper, bell pepper, green tomato and onion left in the garden in the early fall, ground it all up (memories of sitting in the backyard under the big maple trees, the work tables loaded with pans of vegetables, me cranking the grinder), added vinegar and sugar, and then processed it. To anyone now tasting this, you would swear it was a Tex-Mex hot chili salsa. My grandmother didn't know that word. It was "mango relish". People begged for jars of this stuff.