Ritual and superstition do not mean the same thing.
let's say that someone has a behavior whereby: if they enter a house in one door they have to exit through that same door.
To complete your example, let's say they believe that if you do not leave through the same door, you will suffer bad luck.
- The superstition is that if you do not leave through the same door, you will suffer bad luck.
- To avoid bad luck, this person therefore performs the ritual of always leaving through the same door.
The Aztecs used to sacrifice humans to appease the gods.
- The ritual is human sacrifice.
- The superstition is the belief that human sacrifice will appease the gods.
Every Sunday for the last 20 years, we have had a BBQ with our neighbours.
The BBQ can be argued to be a ritual. However, there is no superstition involved here. No one expects negative consequences from failing to show up at the BBQ. They just like attending it.
- A superstition is a belief. More often than not, it either focuses on something that must be done (a ritual) or something that must be avoided (the ritual would then be described as the avoidance of such a situation)
- A ritual is something you do, an action you take. It carries the connotation of being done consistently (or repetitively). It's possible that the reason for the ritual is a superstition, but that is not a guarantee.
An example of a ritual that is not a superstition, is the habit of sports games to start by singing the national anthem.
There is no superstition about singing the national anthem (or failing to do so). It's just a tradition that is being continued.
Let's also say that it was their grandmother's idea, and that they follow it still today, even though they don't know why. That they are anxious about it, and if someone visits, they will gently request that the visitor follows these rules.
Is this superstitious or ritualistic behavior, and why is it either?
As the grandchild sticks to doing this; it is a ritual. It is repetitive behavior that the person chooses to repeat.
Assuming the grandchild has no idea why the grandmother did it, then it cannot be called a superstition. At best, you could call it a tradition (conscious mimicking of the grandmother), or learned behavior (subconscious mimicking of the grandmother, by virtue of never having considered not doing so).
To slightly elaborate:
That they are anxious about it, and if someone visits, they will gently request that the visitor follows these rules.
If the grandchild does not know the reason why it is done; there's no reason for the grandchild to expect other people to also do it.
I think the grandchild can only ask this of other people because they believe failing to do so will bring unwanted consequences (which means they must be aware of the superstition)