Did not S&W make a copy of that submachine gun, by the way? The Model 76 or something like that (this is entirely from memory).
Not really. There is only a very slight superficial resemblance in the layout.
The Madsen sub is a unique design, having a very innovative "clamshell" receiver. Once the barrel nut is removed, the receiver, which is hinged in the rear, opens up like a clamshell to expose all the internal components.
The Smith, on the other hand, is a traditional tube design, and is more or less based on the Swedish K. (I think the K is also known as the Garl Gustav.)