Piperies (Πιπεριές) means peppers, and it is honest to say up front that this is a component, not a sandwich. It earns a place in a sandwich catalog because peppers, grilled or pickled, are one of the recurring building blocks inside Greek wraps and stuffed flatbreads. Treating piperies as a dish in its own right would misrepresent it. What it actually is, is a prepared element with two main forms, and the form changes what it does to whatever it goes into.
The two preparations are distinct and worth getting right. Grilled piperies are charred over direct heat until the skin blisters and blackens, then often peeled, leaving sweet, soft, smoky flesh; the good version is genuinely charred and collapsed, supple and a little oily, while the lazy version is barely marked, still squeaky and raw-tasting, with none of the smoke that justifies the grill. Pickled piperies go the other way: peppers held in a vinegar brine until they are sharp, crisp, and acidic, used in small amounts as a cutting agent against fat and richness. A good pickle keeps some snap and tastes clean; a poor one is flabby, oversweet, or so harsh it flattens everything around it. The whole point of the ingredient is that one form adds sweet smoky body and the other adds bright acidic contrast, and a cook reaches for whichever the larger composition is missing.
Inside a wrap or a stuffed pita this is supporting structure, not the lead. Grilled peppers add softness and sweetness next to grilled meat; pickled peppers cut through fatty fillings and heavy sauces the way a squeeze of lemon would. The dishes they go into, the gyro-style wraps and the stuffed-pita formats, each deserve their own article rather than being crowded in here, since piperies is one line in their build, not the build itself. Read this entry for what the peppers contribute and how to tell a well-made one from a careless one; read it as a component, because that is what it is.