How many models of Asyncronous development in .NET?

There's at least 4, then - a regular callback (non-APM, non-EAP) is also not uncommon

APM - (BeginXXX EndXXX) Which you are using here, when the long running task completes,it calls back into your code in the EndXXX method  
 
EAP - Event based. In this model, when the long running task completes, an event is raised to inform your code. 
 
TPL - New in .NET 4, this is the 'Task' based version. it looks most like Syncronous programming to client code, using a fluent interface. Its calls back to your code using continueWith 

Thread.Start - brutal

delegate.BeginInvoke/EndInvoke - 'old' standard

ThreadPool.QueueUserWorkItem - smart

TaskFactory.StartNew - the only way to do it correct (according to Patterns of parallel programming book | i recommend you to read it first for disambiguation)

The orignal issure address is : http://stackoverflow.com/questions/9271442/how-many-models-of-asyncronous-development-in-net