The definitions are correct – I’m not sure why you’re seeing that post count discrepancy – hopefully one of my colleagues can shed some light.
Yes the Data Explorer plugin is still available and it is well worth installing but it doesn’t replace GA – you use them in tandem. The plugin lets you query any data that we store in your Discourse database. GA will give you organic search data, user journeys, pageviews etc etc.
As an aside, we’re working on an upgrade of our admin dashboard which will give you more digestible data. All going to plan, that will launch with v2.0 early next year.
There are also paid 3rd party services available if you need more data – check out discoursemetrics.com and community-analytics.com