I am not sure this is correct - when you go to
http://brainwallet.org/ and toggle between compressed and uncompressed both the public and private key changes. You cannot use the compressed private key to access the uncompressed public key or vice-verse without changing between the two.
The private key (Wallet Import Format) changes because it is encoded with the flag character to indicate compressed/uncompressed form (see my post above). That 01 suffix changes the base58 value completely.
If you look ate the public key, the uncompressed version starts 04 followed by 128 characters (64 bytes) which are the X and Y coordinates.
Look at the compressed public key and its starts 02 or 03 (which is a flag to indicate the sign of the Y coordainate) followed by the
same X coordinate value as the uncompressed public key.