Since I'm here, I'll take a punt, but I'm no expert (and I expect a cross post will happen by the time I finish).

The public key is a 64 byte (512 bit) number derived by ECC algorithm from the private key. It consists of the X and Y coordinates of a point on the curve. However one of these coordinates is redundant, so the compressed key just uses the X coordinate which shortens the public key length by half. In practice both versions are hashed to 160bit hash value in the block chain. If you take a look at the script I linked above, you can see the procedure for generating both the uncompressed and compressed keys/addresses.

I assume they are equally secure (others may correct me). The reason that only the uncompressed stfu! was compromised is (I guess) that most people just use this one and the hacker did not bother to build the rainbow table for the compressed one (lazy hacker as the ECC is the expensive part, so the only cost of having both is storage space).

Hope this helps. (Yup, crosspost, but not on this topic so I'll post anyway)