Clarifying difference between WCF, REST and SOAP, web API

Dear All, 

I did a lot of research before posting this question, so just as a clarification point of view can you please review the following and let me know if i am heading correct. 

I actually created a WCF project and define few methods inside which are doing something and then made a client then add service reference to that client project and happily consuming the data by calling the methods i defined in the WCF project above, all good till here can you please let me know what shall i call this whether WCF or SOAP API. 

 The reason is someone asked me to create SOAP API for my application so can i say that the one i made above which is working perfectly fine is actually SOAP API as they told me that SOAP API is something which communicates in XML with secured envelope and other fixed format stuff so how i can make this kind of API do i need to completely change my logic if so then what is the above explained API is ? and what is the WebAPI terminology means?

Lastly again another application vendors asked to have the REST API for my application as well, i think i can define some REST functionality in my WCF project and ask to consume by not adding service reference and method calling but through REST API functions of PUT, GET in URL is that correct or do i need to create a separate ASP project for REST.

Thanks a lot for your time.