Hmmm, this is all very interesting to read! It seems people have different ideas of the definition of things:
Polyamory: you agree to let your partner love others & directly oppose any restrictions on how you may love them
Open Relationship: Non monogamous relationships which restrict love with others. Casual sex only.
Polyamory: more freedom than open relationships, some poly people do have a lot of rules to restrict their partner's behaviors
Open Relationship: can only have casual sex with others
Note: some people use "open relationship" and "polyamory" interchangeably, so what exactly poly or open means depends on the individuals involved.
Polyamory: can sometimes be very heavy on rules/restrictions
Open Relationship: "anything goes" where there are very few rules to break, includes loving relationships and casual sex
Swinging: casual-sex-only, no-feelings-allowed