An XYZ tile service provides tiles based on a URL template with values substituted in for Zoom Level and X and Y counts of the tile. They are (usually) limited to a fixed projection (usually EPSG:3857).
A WMS provides an image of the map using a set of key value pairs (KVP) to specify which layers, styles, projection and size to use. It is possible to request tiles in this way too as the WMS protocol is stateless.
A WMTS layer provides predefined tiles (like an XYZ service) with an option to use a RESTful templated URL or a KVP request and with a variety of projections and grids.