Can a public key be same as private key?
That's correct. In some cases, you could, if you really wanted, make a public key equal the private key. It would completely negate the benefit of using a public key cryptosystem, though, because access to the public key would imply access to the private key. It would turn it into a crappy symmetric scheme.

As noted in comments, most common RSA implementations set the public exponent to a fixed value, usually a Fermat prime like 3 or 65537. In that case, for an appropriately-sized modulus, there is no chance for the private exponent to equal the public exponent. The private exponent is always larger.