The fashion in which creative artists do business is wide and varied. I run a special effects studio and prop shop (for 20 years) and we usually don't get paid beyond the initial cost of the prop.
You can be "work for hire"... meaning whatever you do belongs to the employer. Or you can negotiate rights if what you're being hired for is your creativity. I did a puppet build for a museum and they wanted to know that they owned the rights to the character I was building for them free and clear. So I charged them more. That was for them to "own" what I had created. I let go of any rights or claims to the image or likeness of the character.
What it comes down to is that there is no standard as long as you have a good agent or lawyer on your negotiating team.
As for making replicas or building "in the style of" or "being stylistically influenced by", they are totally different things. And its true... the intellectual property argument has been flogged to death here, but its pretty complex and there is always someone who isn't completely informed on what its all about. So, when in doubt, don't hesitate to ask questions!
If what you make is identifiable as a replica of a given character, prop, costume,etc. (someone else's intellectual property) you are TECHNICALLY infringing on that property. But just because the law says its illegal doesn't mean that the law is applied equally in every case. In MOST cases of "healthy fan-related activity", rights holders don't get draconian about the law. It isn't worth it. Universal Studios could crack down on every fan who ever made a Serenity Browncoat costume and they'd be perfectly within their legal rights. But what does that get them? Nothing except a big lawyer bill and the enmity of their fans.
MOST of the time, this sort of thing is just ignored. In the case of the R2 builders group, they have been extremely careful to NOT overstep friendly boundaries with Lucasfilm. They do not manufacture R2-D2s for profit. And they enjoy a level of intimacy with the people of Lucasfilm... even George himself. And groups like the 501st Legion actually participate in Lucasfilm approved events and appearances like the Disney Star Wars Weekends. So in those cases, its all a matter of perspective.
But when someone makes a thousand replicas of that costume and sells them at a profit, the Studio will probably sic a lawyer on them with a "C&D" (Cease and Desist Order). That's just the first warning. Its politely designed to let you know that unless you stop manufacturing or replicating their copyrighted or trademarked items, they will pursue real legal action.
And unless you can convince a judge that what you're making could not be misconstrued as a replica under scrutiny, you're going to have to pay the intellectual property owner some big bucks. That's what they call "damages".
Now, I do puppets. And I use many of the same materials and techniques that the Muppets use. No matter how my design differs from the actual Muppet characters, my works will always have traits in common with them. My vampire puppet, LeShoc, is turquoise, bald, has bat-wing ears, a square nose, wears no cape and is extremely thin. Yet people still walk by and accuse me of "copying" Count Von Count from Sesame Street. Really what they're doing is proving how unfamiliar they are with the design of the REAL Count Von Count considering that I purposely and consciously avoided any details that were replications of those on the Sesame vampire. And when you watch my videos, it is pretty plain to see that this vampire is nothing like The Count. And even if I were manufacturing copies of my Vampire LeShoc, I would be able to stand in front of a judge and defend him as my own design.
Oliver does excellent work on his own original puppets. But somewhere along the line he got the notion that because nobody else was making replicas of Muppets that he could just come along and do it. And he was wrong. And even if he knew what he was doing was illegal, he stupidly thought that the rights owners (namely Disney) would either not find out or would ignore his activity. But its not ever that simple.
Disney found out. Then they waited until they could prove how much money he'd made selling replicas. Then they could really press the case for damages in court. In fact, they probably waited until he had made a really decent amount of money so they could really be sure the prosecution was worth it. Lawyers ain't cheap.
Please notice that Oliver no longer posts images of the Henson-owned Muppets nor the Disney-owned Muppets on his site. Disney and Henson must have cracked down on him. All of the characters he shows are Sesame-owned Muppets and its likely they don't have the budget to sue him for the infraction.
-Gordon