Polyamory has as many different variations as there are poly people. My partner of almost 14 years and I are both polyamorous, but we poly very differently. He tends to be more of a Swolly person, whereas I am more of a Polyfidelitous person. There are so many different types of polyamorous relationships that I can’t even try to list them all, but the image below shows 16 types of polyamorous relationships to consider.
As you can see, polyamory is an umbrella term for relationships that can look very different. This is one reason why I advocate that people who are poly and starting to date have a good discussion about what poly means to them. Labels really only go so far. I’ve known people who thought that they weren’t "really poly" or that they were "doing poly wrong" because they didn’t fit the forms poly that were most visible in their communities. If you fit the definition as provided by Morning Glory Zell (credited with coining the term), you, my friend, are poly! No matter which label fits you best, you’ll probably find that it doesn’t describe all of your relationships with 100% accuracy.
Here is a quick definition of each of the above forms of polyamory.