Whether you are new to steem or a long time member, I find very few people truly understand the entire breadth of the system in regards to the different "forms" of tokens/coins steem uses. I will break down each in an order that will help you to easily get exactly what all these things are!
What is STEEM?
Steem is the base token (currency) built on top of the Steem Blockchain. Steem is liquid, can be sent to anyone at anytime with zero fees! Steem's value floats just like any token relative to supply and demand. Steem is the underlying coin/token that the remainder of the platform is built upon.
Everything is based on STEEM, Think of STEEM as the local currency you use, USD or Euro, etc. STEEM is the base currency for the Steem platform.
What is Steem Power?
STEEM POWER is just like a giant CD or Hedge Fund that you "lock up" your STEEM for a set period of time in exchange for certain rights provided by the fund.
By "Vesting" or "Powering Up" your STEEM, you are trading the ability to instantly sell your STEEM in exchange for more influence on the platform. You give up the liquidity of your base currency "STEEM" in exchange for the right to have more influence when voting on the platform, which in turn gives you more access to earn Curation Rewards!
STEEM POWER locks your STEEM in a VESTED manner that requires a process called Powering Down, which takes 13 weeks, whereby each week 1/13th of your VESTED STEEM is returned to your liquid STEEM balance.
STEEM POWER is the primary location to store your STEEM as it will provide more voting influence, which in turn will lead to greater Curation Rewards.
What is SBD?
SBD or Steem Backed Dollars, are simply a debt, a smart contract technically, that represents an obligation from the blockchain to provide the holder, upon request, $1 worth of STEEM in 3.5 days. SBD when claimed will result in the blockchain creating new STEEM over the next 3.5 days which will be delivered to the holder of the SBD contract while at the same time destroying the SBD.
SBD is simply a "promise" for $1 of STEEM to be paid in 3.5 days from the time it is claimed to the holder from the blockchain. Once the "promise" or more accurately, the "contract", is executed and your STEEM is delivered, the SBD contract is destroyed since it's obligation has been satisfied. This process ensures that as you claim your STEEM from a SBD contract the SBD is destroyed while new STEEM created. This process is explained in much more detail in the white paper as well as steem center (see below for references).
Simply put SBD = ~$1 STEEM. When this rate of exchange drops below $1, SBD should earn interest in your account to account for the exchange rate. SBD Currently does not provide any APR since it is trading well above $1!
Further reading
First read the FAQ specifically the section regarding the currency itself.
I highly advise all to read the White Paper!