These two items are the exact same thing. All that the shop will do is possibly unbolt your existing muffler (the larger and rusted one) and bolt on the new aftermarket muffler. If you welded on the bottom image to the end of the first image, you are going to have a really weird looking setup.
Options are either (a) bolt on the new on after unbolting the old or (b) cutting the old one just before the bowl and welding on the aftermarket.
In any case, as stated before by Lethal, the sound will all depend on the aftermarket muffler you are placing onto your exhaust. You also have the option of adding a silencer afterwards (helps most mufflers from sounding really "ricey" and quiets your **** down a bit lol)
note: the second image doesn't show any hangers so that might need to be welded on in the event you go with option a (assuming for some reason your aftermarket muffler doesn't have them attached).