they are the same, you are just looking at different private key formats
the one you get from bitaddress is a standard WIF (Wallet Import Format) private key,
as the name suggested, this is commonly used for importing privkey-address pair into a wallet
the plain SHA256 gives you a HEX (HEXadecimal) private key
this can be used to import too, but I think not many wallets support importing this format

OP can enter the WIF privkey in the "Wallet Details" tab on bitaddress.org to view all details
it will show all equivalent privkeys in different "Key Formats: WIF, WIFC, HEX, B64, B6, MINI, BIP38"
we can see the AA2D3C4A4A... HEX privkey listed second from the bottom