Spatial data are characterized by a multitude of formats and this variety has always been a problem for interoperability. Together with the need of web access to data, this issue has been the reason for a big standardization effort that brought to the OGC web services aka OWS. These type of services, although a little outdated compared to the increasingly numerous web REST APIs, are well stable and very used by the community of users with a lot of client applications capable of exploiting them. From the technology point of view, OWS services are RPC style services with several possible kind of binding: HTTP GET, POST, HTTP/POX, HTTP/KVP, SOAP via HTTP/POST, but they are surely not RESTful.
From the functional point of view, OWS services can be categorized into two main types: viewing services and access/download services. In the first group we find the WMS, Web Map Service, a service capable of rendering spatial data producing georeferenced images that can be used by map viewers applications. The unit of visualization produced by a WMS is a "layer", and map images are the combination of layers with special rules. It's important to understand that maps are not data, but are representations of data like a HTML page may be the representation of the content of a CMS database.
In the second category we name the WFS (Web Feature Service) and its less known brother WCS (Web Coverage Service). The former delivers vector data to the client and the latter deals with raster coverages.
A query to a WFS or to a WCS produces a download of the original data, or of a subset of it, coded in a suitable transfer format.