If you are authenticating using client x509 certificate against your FTPS server, then you have to store the certificate locally/on client for sure. Without a certificate on client it is not possible to use certificate authentication. Maybe, you didn't store it on disk, but installed in Certificate Storage?
If you are not using client x509 certificate authentication, but only username/password authentication, then there is no need to have any certificate on client. The certificate is needed on FTPS server only (to prove server's identity).
On the other hand, SFTP doesn't need any server certificate. Its identity is verified by the client, typically by checking fingerprint of the server's public key (`Sftp.ServerKey.Fingerprint`).