The way I understand the rules, it seems possible to write a Belief about someone who “logically exist” (one of your character’s parent, for example) without paying Ressources Points during character burning? If so, this makes a NPC appearance without paying the cost… What I understand about relationship is that by paying for one, you are telling the GM and the other players that you want that particular NPC to be part of the Story, but why pay for it if you can do it by writings belief?
… or maybe I do not get at all what relationships are all about…?
When you write a Belief about an NPC that isn’t a relationship, you’re allowing the GM to make all the decisions regarding that person’s status (love/hate, close/distant, important/inconsequential, etc). When you buy a Relationship, you (not the GM) define those details.
It’s all about how much you want control. If you want your parent to be an important person that loves you and will help you, you are going to pay for such.
… so if a player pays for an antagonistic (is that English?) relationship, it has a control over the agenda / motives of that NPC (My Necromancer sister really wants to complete the Wind Of Plagues Rituals). If the player pays for a helping NPC, it has control over how this NPC can help (I saved the elven prince’s butt back in the days).
If you want a helpful relationship you definitely have to pay for it. One big difference is that anyone you want to talk to or meet with requires a Circles roll unless you have a relationship. Maybe that Circles roll would be a Say Yes, but you’re opening the possibility that the person is not available or that today they don’t want to help. Accessibility is still important for antagonistic relationships. You may hate your sister, but it’s different if you can always find her or if she’s sometimes inaccessible.
This isn’t something I’ve thought through much before, but I think the differences go further. Characters brought into existence by Beliefs are there as motivations and obstacles and challenges. If the Wind of Plagues Ritual is a major thing in the story, positive or negative, your sister should be in a Belief and need not be in a relationship. Relationships are for supporting cast, good and bad.
So for the sister example, in a game about stopping an evil necromancer you can have a Belief establishing that the evil necromancer is your sister and is trying to complete a terrible ritual. I then wouldn’t have a relationship. On the other hand, you can have other stuff going on and also have a sister who’s an evil necromancer. That’s a relationship, and you’re opening the door to the GM weaving your evil necromancer sister into other plots, probably mostly as a problem and a hindrance but maybe sometimes as a help.
I would never say that a relationship gives the player control over an NPC. Either a relationship or a Belief can define whether an NPC is positively or negatively inclined towards your character. The former is mostly set in stone—you paid for it with RP—while the latter can change relatively easily—finding out that your “friend” has been against you all along challenges the Belief! But in neither circumstance does the player get real control over what the NPC wants or does. It’s in the GM’s hands, although a paid-for helpful relationship should largely go along with what the player wants, within reason.
These aren’t codified, true statements of the rules. These are just how I’ve been handling it, now written down.
Relationships grant access. If you take a powerful hostile relationship with the Dark Lord, then you can just show up at his Dread Fortress, and he has to come talk to you. He might decide to have you thrown into the torture dungeon afterwards, but you’re important enough to warrant his personal attention.