Does staking of "HBD" different from staking HP?

Yes!
Staking or storing your HBD implies that you'll enjoy the 20% APR plus, since HBD is a stable coin, it usually doesn't drop pass 0.9$ or increase more than 1.1$. the price action in the market doesn't have much effect on HBD compared to Hive.
Staking your Hive gives you premium opportunities on the Blockchain just as I've explained above while HBD is just for the 20 APR and maybe having the assets intact no matter the market condition..

The Hive Power (HP) is automatically staked after you claim your rewards, and can only be totally withdrawn after 13 weeks pending period..

Yes!
A portion of your HP will drop every week until it completes 13weeks for everything to drop.
Take for instance; if you've got 13HP and you're powering down, you'll have 1 Hive every week until everything drops in 13weeks. Hope this is digestible enough?