Difference between Delegatecommand, relaycommand and routedcommand

Your FindProductCommand class implements the ICommand interface, which means it can be used as a WPF command. It is neither a DelegateCommand nor a RelayCommand, nor is it a RoutedCommand, which are other implementations of the ICommand interface.

FindProductCommand vs DelegateCommand/RelayCommand

Generally, when an implementation of ICommand is named DelegateCommand or RelayCommand, the intention is that you don't have to write a class that implements the ICommand interface; rather, you pass the necessary methods as parameters to the DelegateCommand / RelayCommand constructor.

For example, instead of your entire class, you could write:

ProductViewModel _avm;
var FindPoductCommand = new DelegateCommand<object>(
    parameter => _avm.FindProduct(),
    parameter => _avm.CanFindProduct()
);

(Another, perhaps greater benefit than the savings in boilerplate code -- if you instantiate the DelegateCommand / RelayCommand within your viewmodel, your command has access to the internal state of that viewmodel.)

Some implementations of DelegateCommand / RelayCommand:

• Microsoft Prism DelegateCommand reference
• WPF Tutorial implementation of ICommand called DelegateCommand
• Another implementation also called DelegateCommand
• The original implementation of RelayCommand by Josh Smith

Related:

• Relay/ICommand vs DelegateCommand -- Differences

FindProductCommand vs RoutedCommand

Your FindProductCommand will execute FindProduct when triggered.

WPF's built-in RoutedCommand does something else: it raises a routed event which can be handled by other objects in the visual tree. This means you can attach a command binding to those other objects to execute FindProduct, while attaching the RoutedCommand itself specifically to one or more objects that trigger the command, e.g. a button, a menu item, or a context menu item.

Some related SO answers:

• MVVM Routed and Relay Command
• WPF ICommand vs RoutedCommand