Technically, there are a number of different types of battery chargers based on the way they control the charging rate. Chargers are also classified by the level of power they can provide to the battery pack: level 1, 2 and 3.
Based on this "study,("")":http://webfiles.portal.chalmers.se/et/MSc/GrenierMathieuMSc.pdf they identified two types of onboard charger, the unidirectional and bidirectional.