Asynchronous SOAP operation
With asynchronous requests, the client application sends a request to SuiteTalk, where the request is placed in a processing queue and handled asynchronously with other request. The application doesn't wait for the results and the application checks for the results later instead. Each job gets its unique Job ID which can be then used when looking for the results.
An example C# code can be found in Answer 32670: Call Asynchronous Web Service Operation in C#
Synchronous SOAP operation called asynchronously in .NET:
These are just normal NetSuite synchronous SOAP operations called by .NET framework which implements its internal callback mechanism so that the application can continue processing while waiting for the results from server keeping the connection open.
An example C# code can be found in Answer 32669: Call Synchronous Web Service Operation in C# Asynchronously