Well, "prince" can mean different things in different cultures. I'm inclined to believe that was a typo though. Maybe they were confused because of Prince Rilian in the Silver Chair.

Could they have been confused with Prince Rabadash in HHB?

That could be it. Wonder if Rabadash and Rishda were related.  

Wouldn't be surprised if it were a mere slip of the pen. It happens  

Posted by: @jasminetarkheena

That could be it. Wonder if Rabadash and Rishda were related.

While they could be related (after all, nothing's impossible, and they were both Calormenes) I'd go with probably not.  It's easy to forget that they were separated by more than a thousand years, at the very least, and maybe more. I can't remember if Lewis ever gave a definite number of years for the whole Narnian timeline, but there was a large gap between Rilian of the Silver Chair and Tirian,

"Ha!" cried Tirian, "are you then that Eustace and that Jill who rescued King Rilian from his long enchantment?"

"Yes, that's us," said Jill. "So he's King Rilian now, is he? Oh of course he would be. I forgot——"

"Nay," said Tirian, "I am the seventh in descent from him. He has been dead over two hundred years."

Jill made a face. "Ugh!" she said. "That's the horrid part about coming back to Narnia." But Eustace went on.

 and a much larger gap between the Golden Age and Caspian (1300 years?)

He thought of his great-grandfather's great-grandfather, King Rilian....Then he went further back and thought about Rilian's father, Caspian the Seafarer, whose wicked uncle King Miraz had tried to murder him, and how Caspian fled away into the woods and lived among the Dwarfs.... And then he remembered (for he had always been good at history when he was a boy) how those same four children who had helped Caspian had been in Narnia over a thousand years before; and it was then that they had defeated the terrible White Witch and ended the Hundred Years of Winter, and after that they had reigned (all four of them together) at Cair Paravel, till they were no longer children but great Kings and lovely Queens, and their reign had been the golden age of Narnia.

@aileth Maybe it was a slip of the pen. . Wonder what “prince” means in different cultures.  .

It could possibly lead some to speculate that Rabadash and Rishda are the same person, which they are not, like speculations of the White Witch and the Lady of the Green Kirtle being the same person.

Here are the similarities-

1. They were both Calormenes and from the upper class society. Rabadash is the first born of the Tisroc, making him a prince. Suppose Rishda is a prince, maybe in distant relation with whoever was the Tisroc during the events of The Last Battle. It might depend on what the definition of "prince" is in some cultures.

2. They were both arrogant and cruel. Prince Rabadash thinks highly of himself and is willing to shed innocent blood in Archenland, "even down to the last child that was born yesterday". I don't think Rishda have gone that far (unless he had his Calormene soldiers kill innocent children even down to an infant at Cair Paravel). But he still was willing to shed innocent blood.

3. They both have the same motivation; they both wanted to have Narnia for their own or a higher power. They both even use manipulation to get what they want. Prince Rabadash talks his father into allowing him to march the Calormene soldiers to Anvard then to Narnia. Rishda worked closely Shift for a while, then with Ginger. He used manipulation to get the Narnians to join him and the Calormenes in order to make Narnia a Calormene province. He's not the White Witch or the Lady of the Green Kirtle; he doesn't have a magic wand or a magical chair. No, he uses brains and brute strength to get what he wants.

Here are the differences-

1. I don't think Rishda was as childish as Rabadash (unless you count Rishda's reaction when Tash shows up in the stable as childish). Rabadash acts like a child at times when things don't go his way. I never could recall if there was ever a time that Rishda acted like that.

2. They have lived at different time periods. I think over 400 years passed between The Silver Chair and The Last Battle. I'm not sure how much time passed between The Horse and His Boy and The Last Battle. While I still think a relation between Rabadash and Rishda is still a possibility, is still possible they are not.

3. Rabadash was young and a bit of a hot head. I'm not sure how old Rishda was, but I have the impression that he's in his 30's or 40's. Rishda is more manly than Rabadash (at least I think). Rabadash must have been in his late 20's or early 30's.

I never understood the reason why the devotional book Roar: A Christian Family Guide To Narnia referrers to Rishda as Prince Rishda. Maybe "prince" could be another word for "Tarkaan" in that culture or they could have been confused with Prince Rabadash. It's true that they're both Calormenes, but there's no way they could be the same person.

Maybe Netflix could have some implications like, "Oh Rishda Tarkaan, he's in direct descent from the Tisroc Rabadash" or that they are somehow related.  I'm not sure how they would do that, though.

I can only assume that they didn't realise the difference. (both start with R and are Calormenes?)

Focus on the Family used excellent British actors for a variety of accents in the Chronicles series.
Surely they could have asked someone in England whether Prince was a suitable title for Rishda? I think checking this was an oversight.  It would have been fine to use 'Lord',or 'Sir' or a senior military title. After all, they called Shift 'The Lord Shift'.
But I think this was just a mistake.

Posted by: @coracle

I can only assume that they didn't realise the difference. (both start with R and are Calormenes?)

There is that. I actually didn't think about that they both start with R. They also have "sh" in their names (like a majority of Calormenes do- Kidrash, Rishti, Arsheesh, ect). They do have some similarities, like they both wanted to conquer and enslave Narnia.

Focus on the Family used excellent British actors for a variety of accents in the Chronicles series.

I couldn't agree more. At least they didn't cast Russell Boulter or Stash Kirkebride as both characters. I am happy about that. It's no wonder I don't want Netflix to cast the same actor to play both characters. I would like Rishda to be his own villain.

Surely they could have asked someone in England whether Prince was a suitable title for Rishda?

Maybe. As we've kind of already discussed, the word "prince" can mean different things in different cultures. He could be somewhat related to the Tisroc.

I think checking this was an oversight.  It would have been fine to use 'Lord',or 'Sir' or a senior military title. After all, they called Shift 'The Lord Shift'.

I think in the Focus on the Family adaptation, Shift refers to Rishda as "Captain Rishda". It sounds more fitting, because he was the captain of the Calormene army, maybe more than "Prince" or "Sir" or "Lord".