Proactive Maintenance - is focusing on eliminating what causes failure. It is also everything that you do before the equipment goes into service. By going to a Proactive maintenance program you are attacking the root cause and that is what takes a program world class.
Predictive Maintenance - is based on the condition of lubricant or machine. it is monitoring and predicting machine failure. It focuses on recognizing the symptoms of a failure. Predictive maintenance is generally condition based maintenance.
Preventive maintenance - is generally interval/time based maintenance and sometimes can be an opportunity based maintenance (shutdowns, TAs, etc).
Proactive maintenance is generally maintenance tasks generated via studies, analysis, RCA, etc and the purpose is to improve the performance. Of course the studies start in the first place if you feel that there is a need to improve something.