Steem has several types of tokens. Steem, Steem Dollars, and Steem Power (a denomination of VESTS).
When you are paid on the website Steemit, you are paid 50% in STEEM Power, and 50% in STEEM Dollars. Example: If you earn $200 on a post, you will get $100 STEEM Dollars, and 50 STEEM Power (assuming STEEM Power is worth $2 each, at the current time).
It's also possible to receive STEEM tokens through other means, such as VESTS through mining, or transferring STEEM Dollars to someone via STEEM Memo.
Steem is the standard cryptocurrency tradable on various exchanges. It's value can fluctuate just like any other coin.
VESTS (Steem Power)
VESTS are a type of token given to miners, witnesses and content creators/curators. They are denominated as Steem Power on the website Steemit.
They are non-liquid, thus must be "powered down" before being able to trade them. Powering down Steem Power (VESTS) takes 2 years, and is paid out as 104 weekly payments. The power down rate will stay the same if you earn more STEEM Power while powering down, thus it's recommended to re-power down after earning a large amount of fresh STEEM Power.
STEEM Power gains interest over time, and usually gains interest faster than the power down rate, thus you will still be earning interest while powering down.
Steem dollars are a currency which is pegged to the US Dollar. They can be converted on Steemit into STEEM Power (powering up), or into STEEM (easily tradable on various exchanges).