1838 Half Dime - Small Stars & Large Stars

For the Half Dime experts here.... Below is the reference pic from CoinFacts regarding the 1838 Half Dime varieties of large & small stars. Is the picture correct or are the captions
swapped? The reason I ask is because I'm looking at a coin that's for sale with the PCGS slab denoting Large Stars but the coin clearly has what is indicated by this CoinFacts image
to be small stars like the coin shown on the right. The seller's pic is too small to see other diagnostics but the stars can be clearly seen. I don't want to post his pic here to avoid any issues.
I think the CoinFacts image is correct but what do others think? Are the captions reversed? If so then the slab is in error.
swapped? The reason I ask is because I'm looking at a coin that's for sale with the PCGS slab denoting Large Stars but the coin clearly has what is indicated by this CoinFacts image
to be small stars like the coin shown on the right. The seller's pic is too small to see other diagnostics but the stars can be clearly seen. I don't want to post his pic here to avoid any issues.
I think the CoinFacts image is correct but what do others think? Are the captions reversed? If so then the slab is in error.

Great transactions with oih82w8, JasonGaming, Moose1913.
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Since Mr. HalfDime is too busy doing rituals to ensure that the Patriots win the Superbowl, I feel obligated to link this post explaining the die markers for the Small Stars. There are some confusing coins out there that look like the more valuable Small Stars, but aren't. Following Mr. HalfDime's advice is highly recommended.
Detailed answer about diagnostics
Great transactions with oih82w8, JasonGaming, Moose1913.
I do have a question on this though. While the same exist in the dimes of 1838 where the small stars were the stars used on half dimes.......where did the small stars of half dimes come from????