Is it true that if the keys are swapped in RSA, then this is already an EDS implementation?

Question

Encryption

If the RSA algorithm uses a private key instead of a public key for encryption, and an open key instead of a private key for decryption, then this will already be an implementation of electronic signatures , and not confidential data transfer. Everything else in the algorithm remains as before. Can someone explain why the encryption-decryption after changing the places of the private and public keys becomes an electronic signature-verification? In this case, my message is obtained and is not encrypted at all?

Answer 1

The difference is who has access to both keys, and who, respectively, can perform encryption / decryption.
1) Message transmission: anyone can encrypt (with a public key), decrypt - only one (with a private key).
2) EDS: only one person can encrypt (sign), anyone can decrypt (verify the signature).