open marriage and open relationships, in which one or both members of a committed couple may become sexually active with other partners
swinging, similar to open relationships, but commonly conducted as an organised social activity
As can be seen from this list, the Greek prefix 'poly-' (meaning 'many') is often used in naming nonmonogamous forms of relationship. In informal use such names are sometimes abbreviated to just 'poly', with the rest indicated by context.
Many nonmonogamous terms are flexible in definition, because they are based on criteria such as 'relationship' or 'love' that are themselves variably defined; see discussions at their respective pages for more detail on individual forms. In addition, usage creates distinctions beyond the raw definitions of the words. Thus, even though some relationships might technically be considered both polygamous and polyamorous, 'polygamy' usually signifies a codified form of multiple marriage, based on established religious teachings, while 'polyamory' is based on the preferences of the participants rather than social custom or established precedent.