This places the artwork into your Photoshop piece as a "Smart Object" (thus the special symbol in the corner). If you double-click that smart object, it will take you to the source artwork and allow you to edit it. When you save these changes, all Photoshop work that refers to that same Smart Object will update with the latest changes. Smart Objects are also used when importing Illustrator artwork. Double-clicking Smart Objects art made by Illustrator will take you to Illustrator to edit the original source artwork.
Pros: Never lose the original "artwork", allows you to add non-destructive filters (Smart Filters), update the original artwork once and all Photoshop files that refer to the same smart object will also update with the changes made.
Cons: You're not really editing the original pixels of that artwork unless you double-click the Smart Object. A bit more memory overhead.
You're copying and pasting pixel information into a Photoshop layer. No smart objects are created, just a layer containing the pixel information you pasted in. This works like any other Photoshop layer. What you see is what you're actually editing.
Pros: Quick, simple, easy - what's there is really there.
Cons: Filters on this layer will be destructive (unless you turn it into a Smart Object) - the underlying pixel information is impacted if you run filters on it. Also you're only editing the information contained in the current open Photoshop file.
Anyway, hope this helps you better understand the differences.