I'm not an expert, but this is my interpretation (I regularly book side trips, am on one right now):

Fares have break points, which essentially is the return point of your fare, example:

LHR-DXB-BKK-HKG-DXB-LHR

This itinerary might not appear to have a clear fare break point, and it depends on the fare construction, but on EK this would generally break at HKG.

Now if you were to try to add another fare from HKG to somehwere else and back I think that would be end-on-end. And if you were to add another fare on the same ticket before or after LHR (start or end of the entire fare) that would be end-on-end.

A side trip is mid-segment, e.g. (real world example, I'm on such a fare right now, mid-side-trip) CPT-DXB-BOM-DXB-MUC-DXB-CPT

Essentially what this is, is a CPT-MUC return fare, but on the way to MUC you're adding a separate round-trip to BOM. This is not end-on-end, but rather a side trip, and a great way to construct multi city fares as you only pay the additional base fare and taxes but not an entire separate set of carrier imposed surcharges. The fare break point is MUC, my side trip is before I even get to MUC (incidentally even though DXB-MUC might be 2 months into the future I won't get the miles for CPT-DXB until I fly to MUC as the miles are awarded for CPT-MUC as a complete segment, on EK, which is a downside of such construction.

Apologies that my examples are all EK, it's the airline I fly most and construct the most complex itineraries on, however fare rules are pretty uniform across the industry