At the primary school I work at (and that DS and DD1 go to) the teacher/midday assistant who was 'first on scene' would take both kids aside and get their version of events and get bleeding child patched up.
With a physical incident like that, it gets automatically referred to the headteacher/deputy who speak to both children. Both parents would be contacted by letter that day. Incident report would be written up and logged on the system (that's my job!).
WRT punishment, the child who got physical with the other would spend lunchtime writing a sorry letter to the other child and filling out a 'What I Can Do Better' sheet (what happened, who with, why did it happen, what I should do next time). If the bleeding child was found to have provoked the other child, they would receive a punishment too, although a less severe one.
Parents are told that the incident was dealth with 'in accordance with our behaviour policy'. They're not told exactly which punishment was meted out to the other child, but it is easy to infer as punishments are standardized across the school (i.e. physical incidents are always dealt with in the same way, provocation is always dealt with the same way) and the actions/consequences rulebook is sent out to parents at the beginning of the year.
Could be that the other child has been punished, but the teacher/head who dealt with it really should have informed you. Likewise, you should have been told by phonecall or note in message book that your child was in an incident.