Please remember that although SOAP is the most common used protocol that web services use, they can sue other protocols, and are not tied down to SOAP.
Depends on what do you mean by "web service". To me, a web service is only a web service if it uses SOAP bindings (SOAP over HTTP, SOAP over SMTP, SOAP over TCP, SOAP over Flying Doves, etc). In other words, I wouldn't call custom XML over HTTP a web service.