I will make this simple. There is only one question you need to ask yourself or your IT department to determine if what you have is really an Infrastructure-as-a-Service cloud.
Can I get a VM in 5-10 minutes?
Perhaps a little bit more detailed?
Can a properly credentialed user, with a legitimate need for cloud resources, log into your cloud portal or use your cloud API, request a set of cloud resources (compute, network, storage), and have them provisioned for them automatically in a matter of a few minutes (typically less than 10 and often less than 5)?