Stocking Yarn = Sock Yarn?

Dear community,
 are stocking yarn and sock yarn the same? What can both be used for?

I have no idea. Off the top of my head, I’d say that stocking yarn might be thinner, while sock yarn can sometimes be quite thick.

They’re the same thing; it’s just that in some regions they’re called by different names.
Stocking yarn also comes in different weights.

As Hansi writes, they’re exactly the same thing. If you search the internet for “stocking yarn” (I know, people don’t usually search for that here), you’ll find plenty of information about sock yarns.
Stocking and sock yarns are generally available in four different weights:
3-ply, 4-ply, 6-ply, and 8-ply. 

• 3-ply has a yardage of about 500 m per 100 g. It’s hard to find—only a few manufacturers offer it. 
• 4-ply is probably the most common and popular weight. The yardage ranges from 400 to 430 m per 100 g.
• 6-ply has a yardage of 250–260 m per 100 g, and since 100 g isn’t enough for a pair of adult socks, it’s usually sold in 150-g skeins. 
• 8-ply has a yardage of 200–210 m per 100 g, which is half as many meters as 4-ply yarn. It is also usually sold in 150-g skeins. Alternatively, you can use two strands of 4-ply sock yarn; it amounts to the same thing.

Don’t worry, Kruemel-Monster—everyone here knows how to use Google.