Sex vs Relationships: Swing is generally more about recreational sex and polyamory is more about loving relationships. In swinging, friendship is usually the deepest emotional connection that a couple allows with others (and that isn't a requirement for all swingers).  Polyamory usually involves deeply emotional connections (love) with multiple people, and sex can (and usually is) an integral part of those relationships. Swinging is more like friends with benefits, whereas polyamory is more along the lines of having multiple boyfriends, girlfriends or spouses. In polyamory, you open yourself up to falling in LOVE with more than one person at a time. In swing, that's usually pretty threatening to the core couple.

Monogamy vs. Non-monogamy: Swinging, in many ways is still monogamously based. While sexual fidelity isn't a part of that monogamy... swinging is very couple-centric.  A couple goes into it knowing that neither of them will fall for another person any more emotionally than friendship.  Swinging is viewed as safe and non-threatening to the couple's emotionally monogamous relationship. Polyamory usually isn't approached from a couple-centric place.  While couples may both date (even date the same person)... the relationships are viewed as individual relationships.  In polyamory, you're much more an individual than identified with your relationship structure.

Discreet vs. "Out": Swinging is usually a discreet activity that a couple does on the weekends - whereas polyamorous relationship are part of every day life, and not an activity done from time to time.  Usually polyamorous relationships are long term, and have a very regular component to them (daily/weekly, etc.).  Polyamorous people usually have a desire to be "out" about their relationships (even if they can't be realistically) - because the people they're involved with hold a very important place in their lives and heart - equivalent to a spouse/partner/boyfriend/girlfriend.  Poly people tend to want their partners to be with them for for major events - holidays, weddings, funerals, company picnics, etc. - as well as part of their every day life - grocery shopping, movies, hanging out, etc.  

Swinging and Polyamory tend to have a lot of overlap, and there's not a distinct line between the two.  I like to think of it as a continuum - and one end you'll find a few hard core swingers who have a lot of fairly anonymous sex, and at the other end you'll find polyfidelious polys who all live together in a closed relationship. But there's a heck of a lot colors in between the two to choose from.  I've even heard of the term "Swolly" to define folks that are somewhere between swinging and polyamory.  I know poly people who still swing, and I know swingers who have developed poly relationships. And I know plenty of folks who don't worry about the terms, and just go with the flow. 

You don't have to choose one or the other - but they are not the same thing. It's important to be able to communicate with potential new partners about what you desire in relationships.