(1) Is the address generated by www.bitaddress.org a BTC address? Or BCH address (Bitcoin Cash) ?
(2) Is there a general method to recognize BTC address from BCH address?
1) A Bitcoin address/private key is the same as a Bitcoin Cash address/private key.
2) To prevent confusion, one year ago Bitcoin Cash started to use a new address format called CashAddr. They can be used interchangeably if the wallet/service doesn't support the CashAddr format, using the official address translator or mine. Today, most of the services accept both types of the BCH addresses.
To sum up, Bitaddress is compatible with Bitcoin and Bitcoin Cash, but you should convert it to CashAddr before receiving Bitcoin Cash so that they won't send you bitcoins by mistake. (Both
1 and CashAddr addresses are accepted by BCH services while BTC services don't recognize CashAddr, intentionally)
BTW, there's Bitaddress fork named cashaddress.org that generates CashAddr by default.