For these who are familiar with Japan's railway systems - could you explain what are differences between different type commuter intercity and suburban trains?

So far I've seen (based on English translation on display screen and/or articles on wiki and websites): local (that's clear - stops at every stop), 'Rapid', 'Express', 'Limited Express', 'Access Express'.

One more question - these terms/definitions have the same purpose for different train systems/companies, or for example JR East's Express has different meaning than Kaisei Line?