When booking an Economy international flight, is there any difference or benefits between choosing (codeshare) flights operated by United vs say operated by Lufthansa?

If I wanted to change my flights after booking, United says there are no change fees for flights originating in the US. Does that apply to all codeshare flights including those labelled as (e.g.) "Operated by Lufthansa"? How about additional legs that are not codeshare?

Also, does the "no change fee" apply to the full roundtrip itinerary - e.g. if I wanted to later change just the return flight, is that still free of charge, with the first return leg possibly not codeshare, e.g. first leg on Agean, next on UA/LH? Would I be able to change the return flight after taking the outbound flight?