Theoretically both are seems to be same. Hope you are referring InvokeAsync
But I feel their are little difference between them. I will point out what I feel difference.
Begin Invoke is supported from 1.0 framework on the other hand InvokeAsync is fairly newer and supports 2.0 framework onwards.
Starts an asynchronous invocation of an XML Web service method using SOAP while InvokeAsync - Invokes the specified method asynchronously.Additonal information can be supplied by caller using Begin Invoke.
Begin Invoke returns IAsyncResult while InvokeAync is void.