A plugin hybrid can operate as an EV but with a limited all-electric range. The petrol engine is there if you need to exceed that range. Generally they are compromised because you need to drag around both a battery and an engine, so you get the worst of both worlds. The only real attraction is if you don't trust the charging network for longer journeys.
A 'self charging' (aka regular hybrid) is really just a different kind of automatic transmission in a petrol car. It's slightly more efficient, especially at low speed and can have better acceleration, but at the end of the day all the energy comes from petrol. It's a petrol car in a posh frock.
Theo