How do I know if a AWS Server instance has license SQL Server Standard or SQL Server Web?
Run SELECT @@VERSION; in a query window, with results to text. You will see something like this (minor details will vary) in the Messages pane:

Microsoft SQL Server 2014 - 12.0.2402.0 (X64) 
    Aug 13 2014 11:36:34 
    Copyright (c) Microsoft Corporation
    Developer Edition (64-bit) on Windows NT 6.4 &lt;X64&gt; (Build 9841: )
----^^^^^^^^^ edition will be here


Help > About in Management Studio is just about the client tools, so may not even reflect the same version as the server, never mind that Management Studio no longer has any edition differentiations.