They both are same, looks like we still got same legacy nomenclature. The real name is "Teiid Admin Console". It is Grovvy based shell scripting environment, where you can do any administrative tasks as well as issue SQL queries. Teiid Admin Console is also based on Admin API, which is public JAVA API that Teiid exposes, that are you can use in your own applications to customize the interactions with Teiid. BTW, Teiid Designer uses this interface interact with Teiid.
Can you point me to references in documentation for this confusion, I will try to correct them.