Drain the relish. Press your sweet pickle relish in a fine-mesh sieve or with a paper towel. Nobody wants runny sauce.
Mix the wet ingredients. In a small bowl, combine the mayo, drained relish, yellow mustard, vinegar, and sugar. Stir with a fork until smooth and creamy.
Add the dry spices. Sprinkle in the smoked paprika, garlic powder, onion powder, cayenne, and horseradish (if using). Whisk again until the color turns a soft peachy-orange.
Thin it out. Add water one teaspoon at a time until it reaches a thick, drizzle-able milkshake consistency. Don’t overdo it!
Taste & tweak. Dip a fry in there. Need more tang? Add a splash of vinegar. More smoke? Another pinch of paprika.
Let it rest. Cover and refrigerate for at least 30 minutes (overnight is better). The flavors need to marry. Trust the process.