A guilty plea by definition is a conviction
Technically they are not the same.
"They are different stages in the process. The guilty plea is one stage; the sentencing is the final stage and when the actual "conviction" enters. People, of course, also have a right to appeal. People may also elect to file a motion to withdraw their plea. However, sentencing is usually when the offense is treated as a "conviction" and the person is sentenced for the offense. Occasionally, a judge will sentence a person on the same day as a plea. However, with more serious matters (felonies, occasionally some misdemeanor offenses) the judge usually sets the sentencing date for a pre-sentence interview and requests a pre-sentence report prior to sentencing. It should be noted, though, that for certain traffic offenses, the court will send an abstract to the Secretary of State after a plea and before a conviction. This means a person may be facing license sanctions even before their conviction is entered."
Also, a judge has the ability to reject a guilty plea. If someone is convicted, they are already guilty.