If someone pleads guilty to a crime, can they be described as "convicted"?

To put it simply, is "John plead guilty" synonymous with "John was convicted"?

No. The court convicts John. John doesn't convict himself.

John would still be the defendant or the accused.

A person may plea guilty but not be convicted, for example if John was covering for Jane in order to protect her. John could then be convicted of a different crime (preventing the course of justice, interfering with the investigation etc) but not of the crime he plead guilty to.