I think the words are not clear regarding your statements or it may be different in the UK and US systems.
My understanding in the UK is if any offence is 'dismissed' it means you were not 'found' after a trial or 'admitted to' being guilty and therefore you can forget it as it shouldn't appear on any records. If however you admit to the offence or are found guilty you may be given a 'conditional discharge' which would not carry any further penalty if you don't comit a further offence in a given time eg 6 months. Any conditional discharge will remain on record and therefore will show up on a criminal record check.