An interline flight is an agreement between airlines to coordinate passengers with an itinerary that uses multiple airlines, without having to check in again or deal with their baggage at the stopover. The interline relationship is between different legs that can connect.
A codeshare agreement is where airlines operate flights on behalf of another airline, using their flight code. The codeshare relationship is actually on a leg between one operating airline and one or multiple marketing airlines.
A codeshare agreement usually requires an interline agreement so that the marketing carrier can publish a connection with one leg operated by itself and another operated by its codeshare and interline partners.
While the exact terms vary with every partnership, I think the easiest way to sum it up is that an interline agreement is like a friendship, a codeshare agreement is like an engagement, a joint venture is like a marriage, and an alliance is like having a big family, with everyone sort of doing their own thing.
Minimum Connecting time is the amount of transfer time, agreed upon in advance between airlines and airport authorities, that is considered sufficient for a passenger to make a connection between an arriving flight and a departing flight.