HTTPS carries web traffic through TLS, the protocol that protects the connection’s contents and detects changes to them. In ordinary browser use, certificate validation also checks the server’s identity for the requested name.
That establishes a connection to a name; it does not establish that the operator is the bank, shop or person you intended. A deceptive site can have valid HTTPS for its own name. Browser symbols also vary: Chrome’s current guide (opens in a new tab) describes connection-status controls, not a universal padlock test.