I think they are completely different. To me swinging is something that a couple does together and has a strict set of rules under which they operate.
Whereas an in an open marriage the individuals may choose to be married and they may still have a set of rules they follow but they are each able to pursue and enjoy separate relationships on their own outside of their marriage.
For us when we swing it is something we do together and is part of our sex life as a couple. We do not each pursue our own interests or engage in any kind of sex or relationships without the other.
The only thing that separates us from June and Ward Clever ( from the TV show "Leave it to Beaver" for those of you under 35
) is that we sometimes share our bed with others on a purely recreational basis.
Those in open marriages often have "relationships" in addition to their primary marriage. We call ourselves "sexual swingers but emotional monogamists."
Obviously the lines between "open marriage" and "polyamorous" and "swinging separately" etc can get pretty blurry and often overlap at various points.