Actually conditional discharges do appear on your criminal record, for a period of 3 years from the date of the sentencing.
It is there to be considered in the event you break the law in those 3 years.
If you were found not guilty, then there would be no need for a conditional discharge.
A conditional discharge means that they are giving you a second chance and not burdening you with a permanent criminal record.
Usually a conditional discharge is granted when a young, or first time offender commits a "harmless" crime, ie possesion of 1 gram of marijuana, vandalism, shoplifting etc.
If you are convicted of more serious crimes and they want to cut you some slack, they grant you a conditional sentence. Which means you serve your sentence outside of prison, but if you so much as get a speeding ticket, youre off to jail, immediately. You still get a criminal record, but you don‘t actually go to jail, thats the bonus of a conditional sentence.
An absolute discharge is basically like getting off. Only they are not willing to find you NOT GUILTY. You get off scott free, but its understood that you were guilty as charged.
In my day as a juvenile this was called getting your charges "diverted".