NO.
These three terms are
not synonymous.
All three ARE forms of
ethical nonmonogamy or
consensual nonmonogamy or
disclosed nonmonogamy.
Swinging can involve unattached individuals, but usually involves established couples (or even triads, quads, etc.) in group encounters with others, in which the focus is on casual sex. Sure, the people involved can be friends, even close and longtime friends, they might even love each other, but what's going on is that people get together at sex parties.
Open relationships, including open marriages, are relationships in which there is an existing, established bond, but those in the relationship have agreed that they are open to new partners, whether they are short term or long term partners.
There is also
swapping, in which people in a relationship trade partners with people in another relationship, mostly for sex. This is usually done with just two or three couples, as opposed to at a party.
Polyamory means having a romantic, dating, courting, nesting, or spousal relationship with more than one person, with the agreement of all. It takes on many, many forms. It could be a triad who live as spouses to each other. It could involve a married couple who also have girlfriends/boyfriends they see individually or together. It could be four people who are dating each other on an ongoing basis. There are countless forms of polyamory. Some people are polyamorous as an orientation.
Some polyamorous relationships are open. Some are closed. Some polyamorous people engage in swapping and/or swinging, some don't.
Many people who are in open relationships or who swing or swap don't consider themselves polyamorous, especially if they're only looking for casual sex when they get with people outside of their relationships.
There are people in open relationships who are not swingers and do not engage in swapping. There are people who will do swapping but don't consider themselves swingers. There are swingers who do not identify their relationship as open, especially if the only time and place they will get sexual with others is at a swingers club/party.
So, the terms mean different things. And there are other forms of ethical nonmonogamy.
"Yeah, but aren't these all just different words for cheating?"
NO!
Cheating is
breaking the rules.
Ethical or consensual nonmonogamy means that the people involved have
agreements ("rules") that allow for what they are doing.
To be sure, there are people who are involved in these forms of ethical/consensual nonmonogamy who are sometimes involved in cheating, but that is because they broke the rules.
It is up to the people involved in a relationship what the terms of their relationship will be, and if and when those terms will change. As people go through life, their desires and needs can change and they might revisit the terms to modify them.
We need to ensure that adults, regardless of gender, can share love, sex, kink, residence,
and marriage (and any of those things without the others) with any and all consenting adults, without fear of prosecution, bullying, or discrimination. There is
no good reason our laws shouldn't protect these rights, and institutions and service providers need to except and account for the fact that some people are nonmonogamous, and not assume everyone is monogamous or wants monogamy, and certainly not try to force people to be monogamous.