Here's a detailed post authored by an Ethereum researcher (with some bold added)
Casper FFG is what will be introduced in Ethereum first:
Casper the Friendly Finality Gadget (“FFG”) — aka “Vitalik’s
Casper” — is a hybrid PoW/PoS consensus mechanism, which is the
immediate candidate for Ethereum’s first bridge to proof of stake.
More specifically, FFG implements a proof of stake mechanism as an
overlay on top of a proof of work chain (such as Ethereum’s ethash PoW
chain). Simply, the blockchain would grow every block with the
familiar ethash PoW algorithm, but every 50 blocks is a PoS
“checkpoint” where finality is assessed via a network of validators.
Here's a description of Casper CBC:
Casper the Friendly GHOST: Correct-by-Construction (“CBC”) — aka
“Vlad’s Casper”—differs in approach from traditional protocol design:
(1) the protocol is partially specified in the beginning and (2) and
the rest of the protocol is derived in way that is proven to satisfy
the desired/requisite properties (typically protocol is fully defined
then tested to satisfy the said properties). In this case, one way to
derive the full protocol is to implement an estimate safety oracle
(“an ideal adversary”), which either raises exceptions of a fault of a
justified estimate or enumerates the potential future faulty
estimates. More specifically, Vlad’s work focuses on designing
protocols where one can extend local views of a node’s estimate of
safety to achieve consensus safety.
A short rationale:
Taking a step back, FFG focuses more on a multi-step transition to
introducing PoS for the Ethereum network. This prepares for an
iterative implementation that increases the role of PoS in the network
over time. (PoS will claim a smaller portion of the rewards to start).
In contrast, CBC focuses on formal methods that derive safety proofs
“by construction” from first principles. Albeit confusing, the
different approaches to solving this problem created two distinct work
streams that complement each other well. The final form of Casper will
likely draw from learnings from both FFG and CBC.